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http://functions.wolfram.com/07.23.03.1469.01
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Hypergeometric2F1[-(9/2), 5, -(3/2), z] == (1/(1024 (-1 + z)^2))
(1024 + 13 z (1024 +
11 z (2048 + 15 z (-1607 + 7 z (649 + 5 z (-139 + 51 z))))) -
45045 (-1 + z)^2 z^(5/2) (21 - 90 z + 85 z^2) ArcTanh[Sqrt[z]])
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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> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 5 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["9", "2"]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["3", "2"]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric2F1] </annotation> </semantics> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 1024 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 45045 </mn> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 85 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 90 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 21 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 7 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 51 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 139 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 649 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1607 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2048 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1024 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1024 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <cn type='integer'> 5 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 1024 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -45045 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 85 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 90 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 21 </cn> </apply> <apply> <times /> <apply> <power /> <ci> tanh </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 51 </cn> <ci> z </ci> </apply> <cn type='integer'> -139 </cn> </apply> </apply> <cn type='integer'> 649 </cn> </apply> </apply> <cn type='integer'> -1607 </cn> </apply> </apply> <cn type='integer'> 2048 </cn> </apply> </apply> <cn type='integer'> 1024 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 1024 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] | |
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