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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] > Series representations > Generalized power series > Expansions at z==1 > The general formulas





http://functions.wolfram.com/07.28.06.0006.01









  


  










Input Form





HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] == ((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[b, 3]] Gamma[Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]])/(Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]] Gamma[Subscript[a, 3]] Gamma[Subscript[a, 4]])) (1 - z)^(Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3] - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3] - Subscript[a, 4]) (1 + Subscript[d, 1] (z - 1) + Subscript[d, 2] (z - 1)^2 + \[Ellipsis]) + (HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, 1] + ((Subscript[a, 1] Subscript[a, 2] Subscript[a, 3] Subscript[a, 4])/ (Subscript[b, 1] Subscript[b, 2] Subscript[b, 3])) HypergeometricPFQ[{1 + Subscript[a, 1], 1 + Subscript[a, 2], 1 + Subscript[a, 3], 1 + Subscript[a, 4]}, {1 + Subscript[b, 1], 1 + Subscript[b, 2], 1 + Subscript[b, 3]}, 1] (z - 1) + ((Subscript[a, 1] (1 + Subscript[a, 1]) Subscript[a, 2] (1 + Subscript[a, 2]) Subscript[a, 3] (1 + Subscript[a, 3]) Subscript[a, 4] (1 + Subscript[a, 4]))/(2 Subscript[b, 1] (1 + Subscript[b, 1]) Subscript[b, 2] (1 + Subscript[b, 2]) Subscript[b, 3] (1 + Subscript[b, 3]))) HypergeometricPFQ[ {2 + Subscript[a, 1], 2 + Subscript[a, 2], 2 + Subscript[a, 3], 2 + Subscript[a, 4]}, {2 + Subscript[b, 1], 2 + Subscript[b, 2], 2 + Subscript[b, 3]}, 1] (z - 1)^2 + \[Ellipsis]) /; Abs[z - 1] < 1 && Subscript[d, 1] == (Subscript[a, 3] Subscript[a, 4] - Subscript[a, 3] Subscript[b, 1] - Subscript[a, 4] Subscript[b, 1] + Subscript[b, 1]^2 - Subscript[a, 3] Subscript[b, 2] - Subscript[a, 4] Subscript[b, 2] + Subscript[b, 1] Subscript[b, 2] + Subscript[b, 2]^2 + Subscript[a, 2] (Subscript[a, 3] + Subscript[a, 4] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]) + Subscript[a, 1] (Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]) - Subscript[a, 3] Subscript[b, 3] - Subscript[a, 4] Subscript[b, 3] + Subscript[b, 1] Subscript[b, 3] + Subscript[b, 2] Subscript[b, 3] + Subscript[b, 3]^2)/(-1 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]) && Subscript[d, 2] == ((Subscript[a, 1] + Subscript[a, 2] - Subscript[b, 1] - Subscript[b, 2]) (Subscript[a, 1] + Subscript[a, 3] - Subscript[b, 1] - Subscript[b, 2]) (Subscript[a, 2] + Subscript[a, 3] - Subscript[b, 1] - Subscript[b, 2]) + ((-Subscript[a, 3]) Subscript[b, 1] + Subscript[b, 1]^2 + Subscript[a, 2] (Subscript[a, 3] - Subscript[b, 1] - Subscript[b, 2]) + Subscript[a, 1] (Subscript[a, 2] + Subscript[a, 3] - Subscript[b, 1] - Subscript[b, 2]) - Subscript[a, 3] Subscript[b, 2] + Subscript[b, 1] Subscript[b, 2] + Subscript[b, 2]^2) (1 - 2 Subscript[a, 3] + 3 Subscript[b, 1] - Subscript[a, 3] Subscript[b, 1] + Subscript[b, 1]^2 + Subscript[a, 2] (-2 + Subscript[a, 3] - Subscript[b, 1] - Subscript[b, 2]) + Subscript[a, 1] (-2 + Subscript[a, 2] + Subscript[a, 3] - Subscript[b, 1] - Subscript[b, 2]) + 3 Subscript[b, 2] - Subscript[a, 3] Subscript[b, 2] + Subscript[b, 1] Subscript[b, 2] + Subscript[b, 2]^2))/(2 (-2 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3]) (-1 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3])) && !Element[Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3] - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3] - Subscript[a, 4], Integers]










Standard Form





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MathML Form







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<msub> <mi> F </mi> <mn> 3 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> ; </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> </mrow> <mo> ; </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;4&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;3&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox[&quot;a&quot;, &quot;1&quot;], HypergeometricPFQ, Rule[Editable, True]], 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a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> d </mi> <mn> 2 </mn> </msub> <mo> &#10869; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> - </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msubsup> <mi> b </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> - </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msubsup> <mi> b </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> + </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> - </mo> <msub> <mi> a </mi> <mn> 4 </mn> </msub> </mrow> <mo> &#8713; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </list> <list> <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> b </ci> <cn type='integer'> 3 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <plus /> <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> b </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> <apply> <plus /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </list> <list> <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> b </ci> <cn type='integer'> 3 </cn> </apply> </list> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <times /> <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> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </list> <list> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </list> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </list> <list> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </list> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> <apply> <and /> <apply> <lt /> <apply> <abs /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> d </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





© 1998- Wolfram Research, Inc.