|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/06.23.06.0002.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
InverseBetaRegularized[z, a, b] \[Proportional]
InverseBetaRegularized[Subscript[z, 0], a, b] +
(1 - w)^(1 - b) w^(1 - a) Beta[a, b] (z - Subscript[z, 0]) +
(1/2) (1 - w)^(1 - 2 b) w^(1 - 2 a) (1 - a + (-2 + a + b) w) Beta[a, b]^2
(z - Subscript[z, 0])^2 + (1/6) (1 - w)^(1 - 3 b) w^(1 - 3 a)
(1 + 2 a^2 (-1 + w)^2 + (-3 + 2 b) w (2 + (-2 + b) w) +
a (-1 + w) (3 + (-7 + 4 b) w)) Beta[a, b]^3 (z - Subscript[z, 0])^3 +
(1/24) (1 - w)^(1 - 4 b) w^(1 - 4 a) (1 - 6 a + 11 a^2 - 6 a^3 +
(-1 + a) (14 - 11 b + 3 a (-11 + 6 a + 6 b)) w -
3 (-1 + a) (-3 + 2 a + 2 b) (-4 + 3 a + 3 b) w^2 +
(-2 + a + b) (-3 + 2 a + 2 b) (-4 + 3 a + 3 b) w^3) Beta[a, b]^4
(z - Subscript[z, 0])^4 + (1/120) (1 - w)^(1 - 5 b) w^(1 - 5 a)
(1 - 10 a + 35 a^2 - 50 a^3 + 24 a^4 - 2 (-1 + a) (-1 + 2 a)
(15 - 13 b + 2 a (-19 + 12 a + 12 b)) w +
2 (-1 + a) (-75 + 72 a^3 + (121 - 49 b) b + 6 a^2 (-37 + 24 b) +
a (226 + b (-271 + 72 b))) w^2 - 4 (-1 + a) (-3 + 2 a + 2 b)
(-4 + 3 a + 3 b) (-5 + 4 a + 4 b) w^3 + (-2 + a + b) (-3 + 2 a + 2 b)
(-4 + 3 a + 3 b) (-5 + 4 a + 4 b) w^4) Beta[a, b]^5
(z - Subscript[z, 0])^5 + (1/720) (1 - w)^(1 - 6 b) w^(1 - 6 a)
(1 - a (15 + a (-85 + a (225 + 2 a (-137 + 60 a)))) - 62 w +
(a (507 + a (-1622 + a (2547 + 10 a (-197 + 60 a)))) +
3 (-1 + a) (-1 + 2 a) (19 + a (-87 + 100 a)) b) w -
2 (-1 + a) (2 (-3 + 4 a) (-3 + 5 a) (15 + a (-29 + 15 a)) +
(-477 + a (1973 + a (-2681 + 1200 a))) b + (212 - 711 a + 600 a^2)
b^2) w^2 + 2 (-1 + a) (780 +
a (-2943 + 2 a (2066 + 5 a (-257 + 60 a))) - 1923 b +
a (5717 + 3 a (-1859 + 600 a)) b + (1585 + 12 a (-287 + 150 a)) b^2 +
(-437 + 600 a) b^3) w^3 - 5 (-1 + a) (-3 + 2 a + 2 b)
(-4 + 3 a + 3 b) (-5 + 4 a + 4 b) (-6 + 5 a + 5 b) w^4 +
(-2 + a + b) (-3 + 2 a + 2 b) (-4 + 3 a + 3 b) (-5 + 4 a + 4 b)
(-6 + 5 a + 5 b) w^5) Beta[a, b]^6 (z - Subscript[z, 0])^6 +
\[Ellipsis] /; (z -> Subscript[z, 0]) && w =
InverseBetaRegularized[Subscript[z, 0], a, b]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["InverseBetaRegularized", "[", RowBox[List["z", ",", "a", ",", "b"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["InverseBetaRegularized", "[", RowBox[List[SubscriptBox["z", "0"], ",", "a", ",", "b"]], "]"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "w"]], ")"]], RowBox[List["1", "-", "b"]]], " ", SuperscriptBox["w", RowBox[List["1", "-", "a"]]], " ", RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "w"]], ")"]], RowBox[List["1", "-", RowBox[List["2", " ", "b"]]]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["2", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", "a", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "a", "+", "b"]], ")"]], " ", "w"]]]], ")"]], " ", SuperscriptBox[RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "2"]]], "+", RowBox[List[FractionBox["1", "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "w"]], ")"]], RowBox[List["1", "-", RowBox[List["3", " ", "b"]]]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["3", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "w"]], ")"]], "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", "w", " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "b"]], ")"]], " ", "w"]]]], ")"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "w"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "7"]], "+", RowBox[List["4", " ", "b"]]]], ")"]], " ", "w"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], "3"], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "3"]]], "+", RowBox[List[FractionBox["1", "24"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "w"]], ")"]], RowBox[List["1", "-", RowBox[List["4", " ", "b"]]]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["4", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["6", " ", "a"]], "+", RowBox[List["11", " ", SuperscriptBox["a", "2"]]], "-", RowBox[List["6", " ", SuperscriptBox["a", "3"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["14", "-", RowBox[List["11", " ", "b"]], "+", RowBox[List["3", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["6", " ", "a"]], "+", RowBox[List["6", " ", "b"]]]], ")"]]]]]], ")"]], " ", "w"]], "-", RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["3", " ", "a"]], "+", RowBox[List["3", " ", "b"]]]], ")"]], " ", SuperscriptBox["w", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["3", " ", "a"]], "+", RowBox[List["3", " ", "b"]]]], ")"]], " ", SuperscriptBox["w", "3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], "4"], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "4"]]], "+", RowBox[List[FractionBox["1", "120"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "w"]], ")"]], RowBox[List["1", "-", RowBox[List["5", " ", "b"]]]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["5", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["10", " ", "a"]], "+", RowBox[List["35", " ", SuperscriptBox["a", "2"]]], "-", RowBox[List["50", " ", SuperscriptBox["a", "3"]]], "+", RowBox[List["24", " ", SuperscriptBox["a", "4"]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "a"]]]], ")"]], " ", RowBox[List["(", RowBox[List["15", "-", RowBox[List["13", " ", "b"]], "+", RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "19"]], "+", RowBox[List["12", " ", "a"]], "+", RowBox[List["12", " ", "b"]]]], ")"]]]]]], ")"]], " ", "w"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "75"]], "+", RowBox[List["72", " ", SuperscriptBox["a", "3"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["121", "-", RowBox[List["49", " ", "b"]]]], ")"]], " ", "b"]], "+", RowBox[List["6", " ", SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "37"]], "+", RowBox[List["24", " ", "b"]]]], ")"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["226", "+", RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "271"]], "+", RowBox[List["72", " ", "b"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["w", "2"]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["3", " ", "a"]], "+", RowBox[List["3", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["4", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]], ")"]], " ", SuperscriptBox["w", "3"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["3", " ", "a"]], "+", RowBox[List["3", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["4", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]], ")"]], " ", SuperscriptBox["w", "4"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], "5"], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "5"]]], "+", RowBox[List[FractionBox["1", "720"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "w"]], ")"]], RowBox[List["1", "-", RowBox[List["6", " ", "b"]]]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["6", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["a", " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "85"]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["225", "+", RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "137"]], "+", RowBox[List["60", " ", "a"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["62", " ", "w"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["a", " ", RowBox[List["(", RowBox[List["507", "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1622"]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["2547", "+", RowBox[List["10", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "197"]], "+", RowBox[List["60", " ", "a"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "a"]]]], ")"]], " ", RowBox[List["(", RowBox[List["19", "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "87"]], "+", RowBox[List["100", " ", "a"]]]], ")"]]]]]], ")"]], " ", "b"]]]], ")"]], " ", "w"]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["4", " ", "a"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["5", " ", "a"]]]], ")"]], " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "29"]], "+", RowBox[List["15", " ", "a"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "477"]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["1973", "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2681"]], "+", RowBox[List["1200", " ", "a"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", "b"]], "+", RowBox[List[RowBox[List["(", RowBox[List["212", "-", RowBox[List["711", " ", "a"]], "+", RowBox[List["600", " ", SuperscriptBox["a", "2"]]]]], ")"]], " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", SuperscriptBox["w", "2"]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["780", "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2943"]], "+", RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List["2066", "+", RowBox[List["5", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "257"]], "+", RowBox[List["60", " ", "a"]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["1923", " ", "b"]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["5717", "+", RowBox[List["3", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1859"]], "+", RowBox[List["600", " ", "a"]]]], ")"]]]]]], ")"]], " ", "b"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1585", "+", RowBox[List["12", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "287"]], "+", RowBox[List["150", " ", "a"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["b", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "437"]], "+", RowBox[List["600", " ", "a"]]]], ")"]], " ", SuperscriptBox["b", "3"]]]]], ")"]], " ", SuperscriptBox["w", "3"]]], "-", RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["3", " ", "a"]], "+", RowBox[List["3", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["4", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", RowBox[List["5", " ", "a"]], "+", RowBox[List["5", " ", "b"]]]], ")"]], " ", SuperscriptBox["w", "4"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["3", " ", "a"]], "+", RowBox[List["3", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["4", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", RowBox[List["5", " ", "a"]], "+", RowBox[List["5", " ", "b"]]]], ")"]], " ", SuperscriptBox["w", "5"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], "6"], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "6"]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List["z", "\[Rule]", SubscriptBox["z", "0"]]], ")"]], "\[And]", "w"]]]], "=", RowBox[List["InverseBetaRegularized", "[", RowBox[List[SubscriptBox["z", "0"], ",", "a", ",", "b"]], "]"]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <msubsup> <semantics> <mi> I </mi> <annotation-xml encoding='MathML-Content'> <ci> BetaRegularized </ci> </annotation-xml> </semantics> <mi> z </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mrow> <msubsup> <semantics> <mi> I </mi> <annotation-xml encoding='MathML-Content'> <ci> BetaRegularized </ci> </annotation-xml> </semantics> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <semantics> <mi> Β </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <semantics> <mi> Β </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 6 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> w </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <semantics> <mi> Β </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 24 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 11 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 11 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 14 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <semantics> <mi> Β </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 120 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 50 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 35 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 72 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 24 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 37 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 72 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 271 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 226 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 121 </mn> <mo> - </mo> <mrow> <mn> 49 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 75 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 13 </mn> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 19 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 15 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <semantics> <mi> Β </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> <mo> ⁢ </mo> <mtext> </mtext> <msup> <mrow> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 720 </mn> </mfrac> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> w </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 600 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 437 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> b </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 12 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 150 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 287 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1585 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 600 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 1859 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 5717 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 1923 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 257 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2066 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 2943 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 780 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 600 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 711 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mn> 212 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1200 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 2681 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1973 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 477 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 29 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 15 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 10 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 197 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2547 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1622 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 507 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 100 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 87 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 19 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> - </mo> <mrow> <mn> 62 </mn> <mo> ⁢ </mo> <mi> w </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 60 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mn> 137 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 225 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 85 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 15 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <semantics> <mi> Β </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> </msup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mn> 6 </mn> </msup> </mrow> <mtext> </mtext> <mo> + </mo> <mo> … </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <msub> <mi> z </mi> <mn> 0 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ∧ </mo> <mi> w </mi> </mrow> </mrow> <mo> = </mo> <mrow> <msubsup> <semantics> <mi> I </mi> <annotation-xml encoding='MathML-Content'> <ci> BetaRegularized </ci> </annotation-xml> </semantics> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Set </ci> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> InverseBetaRegularized </ci> <ci> z </ci> <ci> a </ci> <ci> b </ci> </apply> <apply> <plus /> <apply> <ci> InverseBetaRegularized </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <ci> a </ci> <ci> b </ci> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <ci> Beta </ci> <ci> a </ci> <ci> b </ci> </apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> <ci> w </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Beta </ci> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 6 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> w </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <cn type='integer'> -7 </cn> </apply> <ci> w </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> w </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> -3 </cn> </apply> <ci> w </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> <ci> w </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Beta </ci> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 24 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -6 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <ci> a </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> b </ci> </apply> <cn type='integer'> -4 </cn> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> b </ci> </apply> <cn type='integer'> -4 </cn> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -11 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <ci> b </ci> </apply> <cn type='integer'> -11 </cn> </apply> </apply> <cn type='integer'> 14 </cn> </apply> <ci> w </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Beta </ci> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 120 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 50 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10 </cn> <ci> a </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> b </ci> </apply> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <cn type='integer'> -5 </cn> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> b </ci> </apply> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <cn type='integer'> -5 </cn> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 72 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 24 </cn> <ci> b </ci> </apply> <cn type='integer'> -37 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 72 </cn> <ci> b </ci> </apply> <cn type='integer'> -271 </cn> </apply> </apply> <cn type='integer'> 226 </cn> </apply> <ci> a </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <plus /> <cn type='integer'> 121 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 49 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -75 </cn> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -13 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <ci> b </ci> </apply> <cn type='integer'> -19 </cn> </apply> </apply> <cn type='integer'> 15 </cn> </apply> <ci> w </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Beta </ci> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 720 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> w </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> b </ci> </apply> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <cn type='integer'> -5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <ci> b </ci> </apply> <cn type='integer'> -6 </cn> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <ci> b </ci> </apply> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <cn type='integer'> -5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <ci> b </ci> </apply> <cn type='integer'> -6 </cn> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 600 </cn> <ci> a </ci> </apply> <cn type='integer'> -437 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 150 </cn> <ci> a </ci> </apply> <cn type='integer'> -287 </cn> </apply> </apply> <cn type='integer'> 1585 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 600 </cn> <ci> a </ci> </apply> <cn type='integer'> -1859 </cn> </apply> </apply> <cn type='integer'> 5717 </cn> </apply> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1923 </cn> <ci> b </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 60 </cn> <ci> a </ci> </apply> <cn type='integer'> -257 </cn> </apply> </apply> <cn type='integer'> 2066 </cn> </apply> </apply> <cn type='integer'> -2943 </cn> </apply> </apply> <cn type='integer'> 780 </cn> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 600 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 711 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> 212 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 1200 </cn> <ci> a </ci> </apply> <cn type='integer'> -2681 </cn> </apply> </apply> <cn type='integer'> 1973 </cn> </apply> </apply> <cn type='integer'> -477 </cn> </apply> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> a </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> a </ci> </apply> <cn type='integer'> -29 </cn> </apply> </apply> <cn type='integer'> 15 </cn> </apply> </apply> </apply> <apply> <power /> <ci> w </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 60 </cn> <ci> a </ci> </apply> <cn type='integer'> -197 </cn> </apply> </apply> <cn type='integer'> 2547 </cn> </apply> </apply> <cn type='integer'> -1622 </cn> </apply> </apply> <cn type='integer'> 507 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 100 </cn> <ci> a </ci> </apply> <cn type='integer'> -87 </cn> </apply> </apply> <cn type='integer'> 19 </cn> </apply> <ci> b </ci> </apply> </apply> <ci> w </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 62 </cn> <ci> w </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 60 </cn> <ci> a </ci> </apply> <cn type='integer'> -137 </cn> </apply> </apply> <cn type='integer'> 225 </cn> </apply> </apply> <cn type='integer'> -85 </cn> </apply> </apply> <cn type='integer'> 15 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Beta </ci> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <apply> <power /> <ci> w </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 6 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <and /> <apply> <ci> Rule </ci> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> <ci> w </ci> </apply> </apply> <apply> <ci> InverseBetaRegularized </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <ci> a </ci> <ci> b </ci> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["InverseBetaRegularized", "[", RowBox[List["z", ",", "a", ",", "b"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["InverseBetaRegularized", "[", RowBox[List[SubscriptBox["z", "0"], ",", "a", ",", "b"]], "]"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "w"]], ")"]], RowBox[List["1", "-", "b"]]], " ", SuperscriptBox["w", RowBox[List["1", "-", "a"]]], " ", RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "w"]], ")"]], RowBox[List["1", "-", RowBox[List["2", " ", "b"]]]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["2", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", "a", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "a", "+", "b"]], ")"]], " ", "w"]]]], ")"]], " ", SuperscriptBox[RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "2"]]], "+", RowBox[List[FractionBox["1", "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "w"]], ")"]], RowBox[List["1", "-", RowBox[List["3", " ", "b"]]]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["3", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "w"]], ")"]], "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", "w", " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "b"]], ")"]], " ", "w"]]]], ")"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "w"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "7"]], "+", RowBox[List["4", " ", "b"]]]], ")"]], " ", "w"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "3"]]], "+", RowBox[List[FractionBox["1", "24"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "w"]], ")"]], RowBox[List["1", "-", RowBox[List["4", " ", "b"]]]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["4", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["6", " ", "a"]], "+", RowBox[List["11", " ", SuperscriptBox["a", "2"]]], "-", RowBox[List["6", " ", SuperscriptBox["a", "3"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["14", "-", RowBox[List["11", " ", "b"]], "+", RowBox[List["3", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "11"]], "+", RowBox[List["6", " ", "a"]], "+", RowBox[List["6", " ", "b"]]]], ")"]]]]]], ")"]], " ", "w"]], "-", RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["3", " ", "a"]], "+", RowBox[List["3", " ", "b"]]]], ")"]], " ", SuperscriptBox["w", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["3", " ", "a"]], "+", RowBox[List["3", " ", "b"]]]], ")"]], " ", SuperscriptBox["w", "3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "4"]]], "+", RowBox[List[FractionBox["1", "120"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "w"]], ")"]], RowBox[List["1", "-", RowBox[List["5", " ", "b"]]]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["5", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["10", " ", "a"]], "+", RowBox[List["35", " ", SuperscriptBox["a", "2"]]], "-", RowBox[List["50", " ", SuperscriptBox["a", "3"]]], "+", RowBox[List["24", " ", SuperscriptBox["a", "4"]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "a"]]]], ")"]], " ", RowBox[List["(", RowBox[List["15", "-", RowBox[List["13", " ", "b"]], "+", RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "19"]], "+", RowBox[List["12", " ", "a"]], "+", RowBox[List["12", " ", "b"]]]], ")"]]]]]], ")"]], " ", "w"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "75"]], "+", RowBox[List["72", " ", SuperscriptBox["a", "3"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["121", "-", RowBox[List["49", " ", "b"]]]], ")"]], " ", "b"]], "+", RowBox[List["6", " ", SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "37"]], "+", RowBox[List["24", " ", "b"]]]], ")"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["226", "+", RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "271"]], "+", RowBox[List["72", " ", "b"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["w", "2"]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["3", " ", "a"]], "+", RowBox[List["3", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["4", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]], ")"]], " ", SuperscriptBox["w", "3"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["3", " ", "a"]], "+", RowBox[List["3", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["4", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]], ")"]], " ", SuperscriptBox["w", "4"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "5"]]], "+", RowBox[List[FractionBox["1", "720"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "w"]], ")"]], RowBox[List["1", "-", RowBox[List["6", " ", "b"]]]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["6", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["a", " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "85"]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["225", "+", RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "137"]], "+", RowBox[List["60", " ", "a"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["62", " ", "w"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["a", " ", RowBox[List["(", RowBox[List["507", "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1622"]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["2547", "+", RowBox[List["10", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "197"]], "+", RowBox[List["60", " ", "a"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "a"]]]], ")"]], " ", RowBox[List["(", RowBox[List["19", "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "87"]], "+", RowBox[List["100", " ", "a"]]]], ")"]]]]]], ")"]], " ", "b"]]]], ")"]], " ", "w"]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["4", " ", "a"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["5", " ", "a"]]]], ")"]], " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "29"]], "+", RowBox[List["15", " ", "a"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "477"]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["1973", "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2681"]], "+", RowBox[List["1200", " ", "a"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", "b"]], "+", RowBox[List[RowBox[List["(", RowBox[List["212", "-", RowBox[List["711", " ", "a"]], "+", RowBox[List["600", " ", SuperscriptBox["a", "2"]]]]], ")"]], " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", SuperscriptBox["w", "2"]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["780", "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2943"]], "+", RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List["2066", "+", RowBox[List["5", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "257"]], "+", RowBox[List["60", " ", "a"]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["1923", " ", "b"]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List["5717", "+", RowBox[List["3", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1859"]], "+", RowBox[List["600", " ", "a"]]]], ")"]]]]]], ")"]], " ", "b"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1585", "+", RowBox[List["12", " ", "a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "287"]], "+", RowBox[List["150", " ", "a"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox["b", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "437"]], "+", RowBox[List["600", " ", "a"]]]], ")"]], " ", SuperscriptBox["b", "3"]]]]], ")"]], " ", SuperscriptBox["w", "3"]]], "-", RowBox[List["5", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["3", " ", "a"]], "+", RowBox[List["3", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["4", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", RowBox[List["5", " ", "a"]], "+", RowBox[List["5", " ", "b"]]]], ")"]], " ", SuperscriptBox["w", "4"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "+", RowBox[List["3", " ", "a"]], "+", RowBox[List["3", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["4", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", RowBox[List["5", " ", "a"]], "+", RowBox[List["5", " ", "b"]]]], ")"]], " ", SuperscriptBox["w", "5"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "6"]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List["z", "\[Rule]", SubscriptBox["z", "0"]]], ")"]], "&&", "w"]]]], "=", RowBox[List["InverseBetaRegularized", "[", RowBox[List[SubscriptBox["z", "0"], ",", "a", ",", "b"]], "]"]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|