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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.aacc.01

 Input Form

 HypergeometricPFQ[{-(5/2), 1/2, 1/2}, {1/2, 4}, -z] == (32 (-8 - 53 z - 173 z^2 + 173 z^3 + 53 z^4 + 8 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(3465 Pi z^3) + (32 Sqrt[1 + z] (-8 - 53 z - 173 z^2 + 173 z^3 + 53 z^4 + 8 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(3465 Pi z^3) + (128 Sqrt[1 + z] (2 + 13 z + 150 z^2 + 13 z^3 + 2 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(3465 Pi z^3) - (64 (-4 - 27 z + 127 z^2 + 199 z^3 + 57 z^4 + 8 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(3465 Pi z^3)

 Standard Form

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 MathML Form

 3 F 2 ( - 5 2 , 1 2 , 1 2 ; 1 2 , 4 ; - z ) 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["5", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "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[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", 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] 32 z + 1 ( 8 z 5 + 53 z 4 + 173 z 3 - 173 z 2 - 53 z - 8 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 3465 π z 3 + 32 ( 8 z 5 + 53 z 4 + 173 z 3 - 173 z 2 - 53 z - 8 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 3465 π z 3 + 128 z + 1 ( 2 z 4 + 13 z 3 + 150 z 2 + 13 z + 2 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 3465 π z 3 - 64 ( 8 z 5 + 57 z 4 + 199 z 3 + 127 z 2 - 27 z - 4 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 3465 π z 3 HypergeometricPFQ -1 5 2 1 2 1 2 1 2 4 -1 z 32 z 1 1 2 8 z 5 53 z 4 173 z 3 -1 173 z 2 -1 53 z -8 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 3465 z 3 -1 32 8 z 5 53 z 4 173 z 3 -1 173 z 2 -1 53 z -8 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 3465 z 3 -1 128 z 1 1 2 2 z 4 13 z 3 150 z 2 13 z 2 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 3465 z 3 -1 -1 64 8 z 5 57 z 4 199 z 3 127 z 2 -1 27 z -4 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 3465 z 3 -1 [/itex]

 Rule Form

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

 2007-05-02