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http://functions.wolfram.com/06.21.06.0055.01
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BetaRegularized[z, a, b] \[Proportional]
Piecewise[{{(z^a (-z)^(b - 1))/((a + b - 1) Beta[a, b]) -
((Sin[a Pi]/Pi) z^a (Log[-z] - PolyGamma[a] + PolyGamma[a + b]))/
(-z)^a, Element[a + b - 1, Integers] && a + b - 1 > 0},
{((Sin[Pi a]/Pi) z^a (Log[-z] - PolyGamma[a] - EulerGamma))/(-z)^a -
(a Sin[Pi a] z^(a - 1))/((-z)^a Pi), a + b == 1},
{(-((-a)!/((-a - b)! (b - 1)!))) (z^(a + b - 1)/(a + b - 1)),
Element[-a, Integers] && -a > 0 && Element[b, Integers] && b > 0 &&
a + b <= 0}, {1, Element[-a, Integers] && -a > 0 &&
Element[b, Integers] && b > 0 && a + b > 0}},
(Csc[Pi (a + b)] Sin[b Pi] z^a)/(-z)^a + (z^a (-z)^(b - 1))/
((a + b - 1) Beta[a, b])] /; (Abs[z] -> Infinity)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BetaRegularized", "[", RowBox[List["z", ",", "a", ",", "b"]], "]"]], "\[Proportional]", RowBox[List["Piecewise", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", "a"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["b", "-", "1"]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", "1"]], ")"]], RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]], " "]]], "-", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List["a", " ", "\[Pi]"]], "]"]], "\[Pi]"], SuperscriptBox["z", "a"], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "a"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", "z"]], "]"]], "-", RowBox[List["PolyGamma", "[", "a", "]"]], "+", RowBox[List["PolyGamma", "[", RowBox[List["a", "+", "b"]], "]"]]]], ")"]]]]]], ",", RowBox[List[RowBox[List[RowBox[List["a", "+", "b", "-", "1"]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List["a", "+", "b", "-", "1"]], ">", "0"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "a"]], "]"]], "\[Pi]"], SuperscriptBox["z", "a"], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "a"]]], RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", "z"]], "]"]], "-", RowBox[List["PolyGamma", "[", "a", "]"]], "-", "EulerGamma"]], ")"]]]], "-", FractionBox[RowBox[List["a", " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "a"]], "]"]], SuperscriptBox["z", RowBox[List["a", "-", "1"]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "a"]]]]], "\[Pi]"]]], ",", RowBox[List[RowBox[List["a", "+", "b"]], "\[Equal]", "1"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["-", "a"]], ")"]], "!"]], " "]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "-", "b"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "1"]], ")"]], "!"]]]]]]], FractionBox[SuperscriptBox["z", RowBox[List["a", "+", "b", "-", "1"]]], RowBox[List["(", RowBox[List["a", "+", "b", "-", "1"]], ")"]]]]], ",", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "a"]], ">", "0"]], "&&", RowBox[List["b", "\[Element]", "Integers"]], "&&", RowBox[List["b", ">", "0"]], "&&", RowBox[List[RowBox[List["a", "+", "b"]], "\[LessEqual]", "0"]]]]]], "}"]], ",", "\[IndentingNewLine]", RowBox[List["{", RowBox[List["1", ",", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "a"]], ">", "0"]], "&&", RowBox[List["b", "\[Element]", "Integers"]], "&&", RowBox[List["b", ">", "0"]], "&&", RowBox[List[RowBox[List["a", "+", "b"]], ">", "0"]]]]]], "}"]]]], "}"]], ",", RowBox[List[RowBox[List[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "\[Pi]"]], "]"]], SuperscriptBox["z", "a"], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "a"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["z", "a"], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["b", "-", "1"]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", "1"]], ")"]], RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]]]]]]]]], "]"]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <semantics> <mi> I </mi> <annotation-xml encoding='MathML-Content'> <ci> BetaRegularized </ci> </annotation-xml> </semantics> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mo>  </mo> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <msup> <mi> z </mi> <mi> a </mi> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <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> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> a </mi> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> π </mi> </mfrac> </mrow> </mtd> <mtd> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> a </mi> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> - </mo> <semantics> <mi> ℽ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[List[], EulerGamma]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> π </mi> </mfrac> <mo> - </mo> <mfrac> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> </msup> </mrow> <mi> π </mi> </mfrac> </mrow> </mtd> <mtd> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo>  </mo> <mn> 1 </mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <msup> <mi> z </mi> <mi> a </mi> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <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> </mrow> </mfrac> <mo> + </mo> <mrow> <mrow> <mi> csc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> a </mi> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> </msup> </mrow> </mrow> </mtd> <mtd> <semantics> <mi> True </mi> <annotation encoding='Mathematica'> TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] </annotation> </semantics> </mtd> </mtr> </mtable> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> BetaRegularized </ci> <ci> z </ci> <ci> a </ci> <ci> b </ci> </apply> <piecewise> <piece> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> Beta </ci> <ci> a </ci> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <sin /> <apply> <times /> <ci> a </ci> <pi /> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> PolyGamma </ci> <ci> a </ci> </apply> </apply> <apply> <ci> PolyGamma </ci> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <in /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> </piece> <piece> <apply> <plus /> <apply> <times /> <apply> <sin /> <apply> <times /> <pi /> <ci> a </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <plus /> <apply> <ln /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> PolyGamma </ci> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <eulergamma /> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <sin /> <apply> <times /> <pi /> <ci> a </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> 1 </cn> </apply> </piece> <otherwise> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> Beta </ci> <ci> a </ci> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <csc /> <apply> <times /> <pi /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <ci> b </ci> <pi /> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> </otherwise> </piecewise> </apply> <apply> <ci> Rule </ci> <apply> <abs /> <ci> z </ci> </apply> <infinity /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BetaRegularized", "[", RowBox[List["z_", ",", "a_", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Piecewise]", GridBox[List[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", "a"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["b", "-", "1"]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", "1"]], ")"]], " ", RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]]]]], "-", FractionBox[RowBox[List[RowBox[List["Sin", "[", RowBox[List["a", " ", "\[Pi]"]], "]"]], " ", SuperscriptBox["z", "a"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "a"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", "z"]], "]"]], "-", RowBox[List["PolyGamma", "[", "a", "]"]], "+", RowBox[List["PolyGamma", "[", RowBox[List["a", "+", "b"]], "]"]]]], ")"]]]], "\[Pi]"]]], RowBox[List[RowBox[List[RowBox[List["a", "+", "b", "-", "1"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["a", "+", "b", "-", "1"]], ">", "0"]]]]], List[RowBox[List[FractionBox[RowBox[List[RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "a"]], "]"]], " ", SuperscriptBox["z", "a"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "a"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", "z"]], "]"]], "-", RowBox[List["PolyGamma", "[", "a", "]"]], "-", "EulerGamma"]], ")"]]]], "\[Pi]"], "-", FractionBox[RowBox[List["a", " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "a"]], "]"]], " ", SuperscriptBox["z", RowBox[List["a", "-", "1"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "a"]]]]], "\[Pi]"]]], RowBox[List[RowBox[List["a", "+", "b"]], "\[Equal]", "1"]]], List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["-", "a"]], ")"]], "!"]], " ", SuperscriptBox["z", RowBox[List["a", "+", "b", "-", "1"]]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "-", "b"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "1"]], ")"]], "!"]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "-", "1"]], ")"]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "a"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "a"]], ">", "0"]], "&&", RowBox[List["b", "\[Element]", "Integers"]], "&&", RowBox[List["b", ">", "0"]], "&&", RowBox[List[RowBox[List["a", "+", "b"]], "\[LessEqual]", "0"]]]]], List["1", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "a"]], ">", "0"]], "&&", RowBox[List["b", "\[Element]", "Integers"]], "&&", RowBox[List["b", ">", "0"]], "&&", RowBox[List[RowBox[List["a", "+", "b"]], ">", "0"]]]]], List[RowBox[List[RowBox[List[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "\[Pi]"]], "]"]], " ", SuperscriptBox["z", "a"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["-", "a"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["z", "a"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["b", "-", "1"]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", "1"]], ")"]], " ", RowBox[List["Beta", "[", RowBox[List["a", ",", "b"]], "]"]]]]]]], TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]]]], Rule[ColumnAlignments, List[Left]], Rule[ColumnSpacings, 1.2`], Rule[ColumnWidths, Automatic]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
