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http://functions.wolfram.com/07.23.03.9445.01
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Hypergeometric2F1[-(23/4), -(1/4), 9/2, -z] ==
(8 Sqrt[2] (-3496 - 48944 z - 372761 z^2 - 3146837 z^3 + 10565882 z^4 +
665654 z^5 + 234059 z^6 + 65263 z^7 + 11788 z^8 + 1008 z^9 -
(1/Sqrt[1 + z]) (2 (-1748 - 25346 z - 198398 z^2 - 1663659 z^3 +
849917 z^4 + 2956448 z^5 + 837468 z^6 + 282301 z^7 + 74041 z^8 +
12544 z^9 + 1008 z^10))))/(117380835 z^(7/2) Sqrt[-1 + Sqrt[1 + z]])
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["23", "4"]]], ",", RowBox[List["-", FractionBox["1", "4"]]], ",", FractionBox["9", "2"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List["8", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3496"]], "-", RowBox[List["48944", " ", "z"]], "-", RowBox[List["372761", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3146837", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["10565882", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["665654", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["234059", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["65263", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["11788", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["1008", " ", SuperscriptBox["z", "9"]]], "-", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "+", "z"]]]], RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1748"]], "-", RowBox[List["25346", " ", "z"]], "-", RowBox[List["198398", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1663659", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["849917", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["2956448", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["837468", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["282301", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["74041", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["12544", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["1008", " ", SuperscriptBox["z", "10"]]]]], ")"]]]], ")"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["117380835", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "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> 23 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </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["23", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["1", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["9", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation> </semantics> <mo>  </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1008 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11788 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 65263 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 234059 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 665654 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 10565882 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3146837 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 372761 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 48944 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1008 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 12544 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 74041 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 282301 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 837468 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2956448 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 849917 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1663659 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 198398 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 25346 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 1748 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 3496 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 117380835 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 23 <sep /> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </list> <list> <cn type='rational'> 9 <sep /> 2 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1008 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11788 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 65263 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 234059 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 665654 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10565882 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3146837 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 372761 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 48944 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 1008 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12544 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 74041 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 282301 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 837468 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2956448 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 849917 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1663659 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 198398 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 25346 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1748 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -3496 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 117380835 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["23", "4"]]], ",", RowBox[List["-", FractionBox["1", "4"]]], ",", FractionBox["9", "2"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["8", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3496"]], "-", RowBox[List["48944", " ", "z"]], "-", RowBox[List["372761", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3146837", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["10565882", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["665654", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["234059", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["65263", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["11788", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["1008", " ", SuperscriptBox["z", "9"]]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1748"]], "-", RowBox[List["25346", " ", "z"]], "-", RowBox[List["198398", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1663659", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["849917", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["2956448", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["837468", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["282301", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["74041", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["12544", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["1008", " ", SuperscriptBox["z", "10"]]]]], ")"]]]], SqrtBox[RowBox[List["1", "+", "z"]]]]]], ")"]]]], RowBox[List["117380835", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]]]]]] |
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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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