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http://functions.wolfram.com/07.23.03.a8rl.01
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Hypergeometric2F1[-(21/4), 15/4, -(11/2), z] ==
(1/(1951488 Pi^(3/2)))
(((1/(-1 + z)^4) (2 (487872 - 144144 z - 134904 z^2 - 179949 z^3 -
316206 z^4 - 816541 z^5 - 5295488 z^6 + 23365632 z^7 - 25100288 z^8 +
8388608 z^9) EllipticE[(1/2) (1 - Sqrt[z])]) +
(1/(-1 + z)^4) (2 (487872 - 144144 z - 134904 z^2 - 179949 z^3 -
316206 z^4 - 816541 z^5 - 5295488 z^6 + 23365632 z^7 - 25100288 z^8 +
8388608 z^9) EllipticE[(1/2) (1 + Sqrt[z])]) +
(1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^3))
((-487872 + 243936 Sqrt[z] - 99792 z + 151536 z^(3/2) - 16632 z^2 +
79926 z^(5/2) + 100023 z^3 - 8019 z^(7/2) + 324225 z^4 -
158675 z^(9/2) + 975216 z^5 - 550528 z^(11/2) + 5846016 z^6 -
10242048 z^(13/2) - 13123584 z^7 + 18808832 z^(15/2) + 6291456 z^8 -
8388608 z^(17/2)) EllipticK[(1/2) (1 - Sqrt[z])]) -
(1/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^4))
((-487872 - 243936 Sqrt[z] - 99792 z - 151536 z^(3/2) - 16632 z^2 -
79926 z^(5/2) + 100023 z^3 + 8019 z^(7/2) + 324225 z^4 +
158675 z^(9/2) + 975216 z^5 + 550528 z^(11/2) + 5846016 z^6 +
10242048 z^(13/2) - 13123584 z^7 - 18808832 z^(15/2) + 6291456 z^8 +
8388608 z^(17/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)
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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> 21 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 15 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 11 </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["21", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["15", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["11", "2"]]], 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> 1951488 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8388608 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 25100288 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 23365632 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5295488 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 816541 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 316206 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 179949 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 134904 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 144144 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 487872 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8388608 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 25100288 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 23365632 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5295488 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 816541 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 316206 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 179949 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 134904 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 144144 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 487872 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 8388608 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 17 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6291456 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 18808832 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 15 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 13123584 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10242048 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5846016 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 550528 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 975216 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 158675 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 324225 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8019 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 100023 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 79926 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 16632 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 151536 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 99792 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 243936 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> - </mo> <mn> 487872 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8388608 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 17 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6291456 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 18808832 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 15 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 13123584 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 10242048 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5846016 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 550528 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> 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</math>
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RowBox[List["79926", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["100023", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["8019", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["324225", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["158675", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["975216", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["550528", " ", SuperscriptBox["z", RowBox[List["11", "/", "2"]]]]], "+", RowBox[List["5846016", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["10242048", " ", SuperscriptBox["z", RowBox[List["13", "/", "2"]]]]], "-", RowBox[List["13123584", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["18808832", " ", SuperscriptBox["z", RowBox[List["15", "/", "2"]]]]], "+", RowBox[List["6291456", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["8388608", " ", SuperscriptBox["z", RowBox[List["17", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "4"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], RowBox[List["1951488", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]]]]]] |
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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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