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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.03.au5s.01

 Input Form

 HypergeometricPFQ[{5/2, 5/2, 7/2}, {2, 2}, z] == (32 (2 + 17 z + 2 z^2) EllipticE[1/2 - Sqrt[1 - z]/2]^2)/ (27 Pi^2 (-1 + z)^4 z) + (32 (-2 - 17 z - 2 z^2) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2])/ (27 Pi^2 (-1 + z)^4 z) + (32 Sqrt[1 - z] (7 - 17 z - 92 z^2 - 3 z^3) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2])/ (135 Pi^2 (-1 + z)^5 z) - (112 (1 + 4 z) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/ (135 Pi^2 (-1 + z)^3 z) + (16 Sqrt[1 - z] (-7 + 17 z + 92 z^2 + 3 z^3) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/(135 Pi^2 (-1 + z)^5 z)

 Standard Form

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 MathML Form

 3 F 2 ( 5 2 , 5 2 , 7 2 ; 2 , 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "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["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["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] 32 ( 2 z 2 + 17 z + 2 ) E ( 1 2 - 1 - z 2 ) 2 27 π 2 ( z - 1 ) 4 z + 32 ( - 2 z 2 - 17 z - 2 ) K ( 1 2 - 1 - z 2 ) E ( 1 2 - 1 - z 2 ) 27 π 2 ( z - 1 ) 4 z + 32 1 - z ( - 3 z 3 - 92 z 2 - 17 z + 7 ) K ( 1 2 - 1 - z 2 ) E ( 1 2 - 1 - z 2 ) 135 π 2 ( z - 1 ) 5 z - 112 ( 4 z + 1 ) K ( 1 2 - 1 - z 2 ) 2 135 π 2 ( z - 1 ) 3 z + 16 1 - z ( 3 z 3 + 92 z 2 + 17 z - 7 ) K ( 1 2 - 1 - z 2 ) 2 135 π 2 ( z - 1 ) 5 z HypergeometricPFQ 5 2 5 2 7 2 2 2 z 32 2 z 2 17 z 2 EllipticE 1 2 -1 1 -1 z 1 2 2 -1 2 27 2 z -1 4 z -1 32 -2 z 2 -1 17 z -2 EllipticK 1 2 -1 1 -1 z 1 2 2 -1 EllipticE 1 2 -1 1 -1 z 1 2 2 -1 27 2 z -1 4 z -1 32 1 -1 z 1 2 -3 z 3 -1 92 z 2 -1 17 z 7 EllipticK 1 2 -1 1 -1 z 1 2 2 -1 EllipticE 1 2 -1 1 -1 z 1 2 2 -1 135 2 z -1 5 z -1 -1 112 4 z 1 EllipticK 1 2 -1 1 -1 z 1 2 2 -1 2 135 2 z -1 3 z -1 16 1 -1 z 1 2 3 z 3 92 z 2 17 z -7 EllipticK 1 2 -1 1 -1 z 1 2 2 -1 2 135 2 z -1 5 z -1 [/itex]

 Rule Form

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

 2007-05-02