Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9268)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=-9/4

http://functions.wolfram.com/07.23.03.9268.01

Input Form

Hypergeometric2F1[-(23/4), -(9/4), 6, z] == (1/(17657846952270525 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((9844736 - 189972640 z + 1913200421 z^2 - 14569271915 z^3 + 120210547765 z^4 + 3190541871153 z^5 + 5027880539955 z^6 + 1497730418223 z^7 + 3582470775 z^8 - 234088725 z^9 + 9613500 z^10) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-9844736 + 9844736 Sqrt[z] + 182589088 z - 182589088 z^(3/2) - 1777412285 z^2 + 1777412285 z^(5/2) + 13257177230 z^3 - 13257177230 z^(7/2) - 110468152795 z^4 + 110468152795 z^(9/2) - 1116414650988 z^5 + 1116414650988 z^(11/2) - 1095078835851 z^6 + 1095078835851 z^(13/2) - 152803698450 z^7 + 152803698450 z^(15/2) + 6826065675 z^8 - 6826065675 z^(17/2) - 453757200 z^9 + 453757200 z^(19/2) + 19227000 z^10 - 19227000 z^(21/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["23", "4"]]], ",", RowBox[List["-", FractionBox["9", "4"]]], ",", "6", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["17657846952270525", " ", "\[Pi]", " ", SuperscriptBox["z", "5"]]]], RowBox[List["(", RowBox[List["16384", " ", SqrtBox[RowBox[List["1", "+", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["9844736", "-", RowBox[List["189972640", " ", "z"]], "+", RowBox[List["1913200421", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["14569271915", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["120210547765", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["3190541871153", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["5027880539955", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1497730418223", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["3582470775", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["234088725", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["9613500", " ", SuperscriptBox["z", "10"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["1", "+", SqrtBox["z"]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "9844736"]], "+", RowBox[List["9844736", " ", SqrtBox["z"]]], "+", RowBox[List["182589088", " ", "z"]], "-", RowBox[List["182589088", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["1777412285", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1777412285", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["13257177230", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["13257177230", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["110468152795", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["110468152795", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["1116414650988", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["1116414650988", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["1095078835851", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1095078835851", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "-", RowBox[List["152803698450", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["152803698450", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "+", RowBox[List["6826065675", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["6826065675", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "-", RowBox[List["453757200", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["453757200", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "+", RowBox[List["19227000", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["19227000", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["1", "+", SqrtBox["z"]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

MathML Form

<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> 9 </mn> <mn> 4 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mn> 6 </mn> <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["23", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["9", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["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> <mfrac> <mn> 1 </mn> <mrow> <mn> 17657846952270525 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 16384 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9613500 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 234088725 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3582470775 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1497730418223 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5027880539955 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3190541871153 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 120210547765 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 14569271915 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1913200421 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 189972640 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 9844736 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 19227000 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 21 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 19227000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 453757200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 19 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 453757200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6826065675 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 17 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6826065675 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 152803698450 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 15 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 152803698450 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1095078835851 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1095078835851 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1116414650988 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1116414650988 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 110468152795 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 110468152795 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 13257177230 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13257177230 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1777412285 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1777412285 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 182589088 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 182589088 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 9844736 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> - </mo> <mn> 9844736 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </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'> 9 <sep /> 4 </cn> </apply> </list> <list> <cn type='integer'> 6 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 17657846952270525 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16384 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 9613500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 234088725 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3582470775 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1497730418223 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5027880539955 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3190541871153 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 120210547765 </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'> 14569271915 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1913200421 </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'> 189972640 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 9844736 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -19227000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 21 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 19227000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 453757200 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 453757200 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6826065675 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6826065675 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 152803698450 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 152803698450 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1095078835851 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1095078835851 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1116414650988 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1116414650988 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 110468152795 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 110468152795 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 13257177230 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 13257177230 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1777412285 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1777412285 </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'> 182589088 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 182589088 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 9844736 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -9844736 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["23", "4"]]], ",", RowBox[List["-", FractionBox["9", "4"]]], ",", "6", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["16384", " ", SqrtBox[RowBox[List["1", "+", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["9844736", "-", RowBox[List["189972640", " ", "z"]], "+", RowBox[List["1913200421", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["14569271915", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["120210547765", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["3190541871153", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["5027880539955", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1497730418223", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["3582470775", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["234088725", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["9613500", " ", SuperscriptBox["z", "10"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["1", "+", SqrtBox["z"]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "9844736"]], "+", RowBox[List["9844736", " ", SqrtBox["z"]]], "+", RowBox[List["182589088", " ", "z"]], "-", RowBox[List["182589088", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["1777412285", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1777412285", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["13257177230", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["13257177230", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["110468152795", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["110468152795", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["1116414650988", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["1116414650988", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "-", RowBox[List["1095078835851", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1095078835851", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "-", RowBox[List["152803698450", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["152803698450", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "+", RowBox[List["6826065675", " ", SuperscriptBox["z", "8"]]], "-", RowBox[List["6826065675", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]], "-", RowBox[List["453757200", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["453757200", " ", SuperscriptBox["z", RowBox[List["19", "/", "2"]]]]], "+", RowBox[List["19227000", " ", SuperscriptBox["z", "10"]]], "-", RowBox[List["19227000", " ", SuperscriptBox["z", RowBox[List["21", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["1", "+", SqrtBox["z"]]]], "]"]]]]]], ")"]]]], RowBox[List["17657846952270525", " ", "\[Pi]", " ", SuperscriptBox["z", "5"]]]]]]]]

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

2007-05-02

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,...,a_p},{b₁,...,b_q},z]