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 HypergeometricPFQ

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

 Input Form

 HypergeometricPFQ[{5/2, 5/2, 5/2}, {-(7/2), 2}, -z] == (1/(315 Pi z (1 + z)^9)) (4 (105 + 1206 z + 6750 z^2 + 25776 z^3 + 87249 z^4 + 567666 z^5 - 591680 z^6 + 54656 z^7) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(315 Pi z (1 + z)^(17/2))) (4 (105 + 1206 z + 6750 z^2 + 25776 z^3 + 87249 z^4 + 567666 z^5 - 591680 z^6 + 54656 z^7) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) - (1/(315 Pi z (1 + z)^8)) (16 (105 + 1104 z + 5754 z^2 + 22056 z^3 + 113109 z^4 - 171264 z^5 + 19648 z^6) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) - (1/(315 Pi z (1 + z)^(17/2))) (8 (-105 - 1212 z - 6966 z^2 - 29844 z^3 - 183081 z^4 + 683976 z^5 - 288448 z^6 + 15360 z^7) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])

 Standard Form

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 MathML Form

 3 F 2 ( 5 2 , 5 2 , 5 2 ; - 7 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["5", "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[RowBox[List["-", FractionBox["7", "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[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] 1 315 π z ( z + 1 ) 17 / 2 4 ( 54656 z 7 - 591680 z 6 + 567666 z 5 + 87249 z 4 + 25776 z 3 + 6750 z 2 + 1206 z + 105 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) + 1 315 π z ( z + 1 ) 9 4 ( 54656 z 7 - 591680 z 6 + 567666 z 5 + 87249 z 4 + 25776 z 3 + 6750 z 2 + 1206 z + 105 ) E ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) - 16 ( 19648 z 6 - 171264 z 5 + 113109 z 4 + 22056 z 3 + 5754 z 2 + 1104 z + 105 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) 315 π z ( z + 1 ) 8 - 1 315 π z ( z + 1 ) 17 / 2 8 ( 15360 z 7 - 288448 z 6 + 683976 z 5 - 183081 z 4 - 29844 z 3 - 6966 z 2 - 1212 z - 105 ) K ( ( z + 1 - 1 ) 2 ( z + 1 + 1 ) 2 ) HypergeometricPFQ 5 2 5 2 5 2 -1 7 2 2 -1 z 1 315 z z 1 17 2 -1 4 54656 z 7 -1 591680 z 6 567666 z 5 87249 z 4 25776 z 3 6750 z 2 1206 z 105 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 1 315 z z 1 9 -1 4 54656 z 7 -1 591680 z 6 567666 z 5 87249 z 4 25776 z 3 6750 z 2 1206 z 105 EllipticE z 1 1 2 -1 2 z 1 1 2 1 2 -1 -1 16 19648 z 6 -1 171264 z 5 113109 z 4 22056 z 3 5754 z 2 1104 z 105 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 315 z z 1 8 -1 -1 1 315 z z 1 17 2 -1 8 15360 z 7 -1 288448 z 6 683976 z 5 -1 183081 z 4 -1 29844 z 3 -1 6966 z 2 -1 1212 z -105 EllipticK z 1 1 2 -1 2 z 1 1 2 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02