|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.36.06.0001.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
AppellF1[a, Subscript[b, 1], Subscript[b, 2], c, Subscript[z, 1],
Subscript[z, 2]] \[Proportional] 1 + (a Subscript[b, 1] Subscript[z, 1])/
c + (a (1 + a) Subscript[b, 1] (1 + Subscript[b, 1]) Subscript[z, 1]^2)/
(2 c (1 + c)) + (a Subscript[b, 2] Subscript[z, 2])/c +
(a (1 + a) Subscript[b, 1] Subscript[b, 2] Subscript[z, 1]
Subscript[z, 2])/(c (1 + c)) + (a (1 + a) (2 + a) Subscript[b, 1]
(1 + Subscript[b, 1]) Subscript[b, 2] Subscript[z, 1]^2 Subscript[z, 2])/
(2 c (1 + c) (2 + c)) + (a (1 + a) Subscript[b, 2] (1 + Subscript[b, 2])
Subscript[z, 2]^2)/(2 c (1 + c)) +
(a (1 + a) (2 + a) Subscript[b, 1] Subscript[b, 2] (1 + Subscript[b, 2])
Subscript[z, 1] Subscript[z, 2]^2)/(2 c (1 + c) (2 + c)) +
(a (1 + a) (2 + a) (3 + a) Subscript[b, 1] (1 + Subscript[b, 1])
Subscript[b, 2] (1 + Subscript[b, 2]) Subscript[z, 1]^2
Subscript[z, 2]^2)/(4 c (1 + c) (2 + c) (3 + c)) + \[Ellipsis] /;
(Subscript[z, 1] -> 0) && (Subscript[z, 2] -> 0)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["AppellF1", "[", RowBox[List["a", ",", SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"], ",", "c", ",", SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], "\[Proportional]", RowBox[List["1", "+", FractionBox[RowBox[List["a", " ", SubscriptBox["b", "1"], " ", SubscriptBox["z", "1"]]], "c"], "+", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", SubscriptBox["b", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "1"]]], ")"]], " ", SubsuperscriptBox["z", "1", "2"]]], RowBox[List["2", " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]]]]], "+", FractionBox[RowBox[List["a", " ", SubscriptBox["b", "2"], " ", SubscriptBox["z", "2"]]], "c"], "+", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", SubscriptBox["b", "1"], " ", SubscriptBox["b", "2"], " ", SubscriptBox["z", "1"], " ", SubscriptBox["z", "2"]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]]]]], "+", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "a"]], ")"]], " ", SubscriptBox["b", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "1"]]], ")"]], " ", SubscriptBox["b", "2"], " ", SubsuperscriptBox["z", "1", "2"], " ", SubscriptBox["z", "2"]]], RowBox[List["2", " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "c"]], ")"]]]]], "+", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", SubscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "2"]]], ")"]], " ", SubsuperscriptBox["z", "2", "2"]]], RowBox[List["2", " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]]]]], "+", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "a"]], ")"]], " ", SubscriptBox["b", "1"], " ", SubscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "2"]]], ")"]], " ", SubscriptBox["z", "1"], " ", SubsuperscriptBox["z", "2", "2"]]], RowBox[List["2", " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "c"]], ")"]]]]], "+", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "a"]], ")"]], " ", SubscriptBox["b", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "1"]]], ")"]], " ", SubscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "2"]]], ")"]], " ", SubsuperscriptBox["z", "1", "2"], " ", SubsuperscriptBox["z", "2", "2"]]], RowBox[List["4", " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "c"]], ")"]]]]], "+", "\[Ellipsis]"]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["z", "1"], "\[Rule]", "0"]], ")"]], "\[And]", RowBox[List["(", RowBox[List[SubscriptBox["z", "2"], "\[Rule]", "0"]], ")"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <semantics> <msub> <mi> F </mi> <mn> 1 </mn> </msub> <annotation-xml encoding='MathML-Content'> <ci> AppellF1 </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ; </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <mi> c </mi> <mo> ; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mi> c </mi> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mi> c </mi> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mo> … </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ∧ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> AppellF1 </ci> <ci> a </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> c </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <ci> a </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> a </ci> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> c </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> a </ci> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <ci> c </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> c </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> a </ci> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> c </ci> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> a </ci> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> c </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> a </ci> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> c </ci> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> a </ci> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <plus /> <cn type='integer'> 3 </cn> <ci> a </ci> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> c </ci> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <apply> <plus /> <cn type='integer'> 3 </cn> <ci> c </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> … </ci> </apply> </apply> <apply> <and /> <apply> <ci> Rule </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <ci> Rule </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AppellF1", "[", RowBox[List["a_", ",", SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"], ",", "c_", ",", SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["1", "+", FractionBox[RowBox[List["a", " ", SubscriptBox["bb", "1"], " ", SubscriptBox["zz", "1"]]], "c"], "+", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", SubscriptBox["bb", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "1"]]], ")"]], " ", SubsuperscriptBox["zz", "1", "2"]]], RowBox[List["2", " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]]]]], "+", FractionBox[RowBox[List["a", " ", SubscriptBox["bb", "2"], " ", SubscriptBox["zz", "2"]]], "c"], "+", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", SubscriptBox["bb", "1"], " ", SubscriptBox["bb", "2"], " ", SubscriptBox["zz", "1"], " ", SubscriptBox["zz", "2"]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]]]]], "+", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "a"]], ")"]], " ", SubscriptBox["bb", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "1"]]], ")"]], " ", SubscriptBox["bb", "2"], " ", SubsuperscriptBox["zz", "1", "2"], " ", SubscriptBox["zz", "2"]]], RowBox[List["2", " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "c"]], ")"]]]]], "+", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", SubscriptBox["bb", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "2"]]], ")"]], " ", SubsuperscriptBox["zz", "2", "2"]]], RowBox[List["2", " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]]]]], "+", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "a"]], ")"]], " ", SubscriptBox["bb", "1"], " ", SubscriptBox["bb", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "2"]]], ")"]], " ", SubscriptBox["zz", "1"], " ", SubsuperscriptBox["zz", "2", "2"]]], RowBox[List["2", " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "c"]], ")"]]]]], "+", FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "a"]], ")"]], " ", SubscriptBox["bb", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "1"]]], ")"]], " ", SubscriptBox["bb", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "2"]]], ")"]], " ", SubsuperscriptBox["zz", "1", "2"], " ", SubsuperscriptBox["zz", "2", "2"]]], RowBox[List["4", " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List["3", "+", "c"]], ")"]]]]], "+", "\[Ellipsis]"]], "/;", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["zz", "1"], "\[Rule]", "0"]], ")"]], "&&", RowBox[List["(", RowBox[List[SubscriptBox["zz", "2"], "\[Rule]", "0"]], ")"]]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|