Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1633)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃>=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=3/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=3/2, b₁=1

http://functions.wolfram.com/07.27.03.1633.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 3/2}, {1, 3}, z] == (1/(12006225 Pi^2 z^2)) (64 (-4900 + 73500 z + 10989214 z^2 + 38043220 z^3 + 22092303 z^4 + 1857872 z^5) EllipticE[1/2 - Sqrt[1 - z]/2]^2) + (1/(12006225 Pi^2 z^2)) (64 (4900 - 73500 z - 10989214 z^2 - 38043220 z^3 - 22092303 z^4 - 1857872 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(12006225 Pi^2 z^2)) (64 Sqrt[1 - z] (4900 - 72275 z - 5600334 z^2 - 15553756 z^3 - 7227832 z^4 - 443520 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(12006225 Pi^2 z^2)) (32 Sqrt[1 - z] (-4900 + 72275 z + 5600334 z^2 + 15553756 z^3 + 7227832 z^4 + 443520 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(12006225 Pi^2 z^2)) (32 (-4900 + 74725 z + 7065434 z^2 + 23103334 z^3 + 12879983 z^4 + 1039816 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", FractionBox["7", "2"]]], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", "3"]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["12006225", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List["64", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4900"]], "+", RowBox[List["73500", " ", "z"]], "+", RowBox[List["10989214", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["38043220", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["22092303", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1857872", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]], "2"]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["12006225", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List["64", " ", RowBox[List["(", RowBox[List["4900", "-", RowBox[List["73500", " ", "z"]], "-", RowBox[List["10989214", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["38043220", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["22092303", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1857872", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["12006225", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List["64", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["4900", "-", RowBox[List["72275", " ", "z"]], "-", RowBox[List["5600334", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["15553756", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["7227832", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["443520", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["12006225", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List["32", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4900"]], "+", RowBox[List["72275", " ", "z"]], "+", RowBox[List["5600334", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["15553756", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["7227832", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["443520", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]], "2"]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["12006225", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List["32", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4900"]], "+", RowBox[List["74725", " ", "z"]], "+", RowBox[List["7065434", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["23103334", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["12879983", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1039816", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]], "2"]]], ")"]]]]]]]]]]

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> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mn> 7 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1857872 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 22092303 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 38043220 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 10989214 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 73500 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 4900 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> E </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 12006225 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 12006225 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 1857872 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 22092303 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 38043220 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10989214 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 73500 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 4900 </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> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mn> 2 </mn> </mfrac> </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> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 12006225 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 64 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 443520 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 7227832 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 15553756 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5600334 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 72275 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 4900 </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> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mn> 2 </mn> </mfrac> </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> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 12006225 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mn> 32 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 443520 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7227832 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 15553756 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5600334 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 72275 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 4900 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 32 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1039816 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 12879983 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 23103334 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7065434 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 74725 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 4900 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <mi> K </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mfrac> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mrow> <mn> 12006225 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </list> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 3 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 1857872 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 22092303 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 38043220 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10989214 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 73500 </cn> <ci> z </ci> </apply> <cn type='integer'> -4900 </cn> </apply> <apply> <power /> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 12006225 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 12006225 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1857872 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 22092303 </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'> 38043220 </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'> 10989214 </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'> 73500 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 4900 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 12006225 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -443520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7227832 </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'> 15553756 </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'> 5600334 </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'> 72275 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 4900 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 12006225 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 443520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7227832 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 15553756 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5600334 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 72275 </cn> <ci> z </ci> </apply> <cn type='integer'> -4900 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 1039816 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12879983 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 23103334 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7065434 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 74725 </cn> <ci> z </ci> </apply> <cn type='integer'> -4900 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 12006225 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["7", "2"]]], ",", RowBox[List["-", FractionBox["7", "2"]]], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["1", ",", "3"]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["64", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4900"]], "+", RowBox[List["73500", " ", "z"]], "+", RowBox[List["10989214", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["38043220", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["22092303", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1857872", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]], "2"]]], RowBox[List["12006225", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["64", " ", RowBox[List["(", RowBox[List["4900", "-", RowBox[List["73500", " ", "z"]], "-", RowBox[List["10989214", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["38043220", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["22092303", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["1857872", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]]]], RowBox[List["12006225", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["64", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["4900", "-", RowBox[List["72275", " ", "z"]], "-", RowBox[List["5600334", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["15553756", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["7227832", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["443520", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]]]], RowBox[List["12006225", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["32", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4900"]], "+", RowBox[List["72275", " ", "z"]], "+", RowBox[List["5600334", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["15553756", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["7227832", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["443520", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]], "2"]]], RowBox[List["12006225", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List["32", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "4900"]], "+", RowBox[List["74725", " ", "z"]], "+", RowBox[List["7065434", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["23103334", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["12879983", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["1039816", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], "2"]]], "]"]], "2"]]], RowBox[List["12006225", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", "2"]]]]]]]]]]

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},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},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]