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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.bsk6.01

 Input Form

 Hypergeometric2F1[-(9/8), 21/8, 4, z] == (1/(2734875 Pi z^3)) (1024 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-384 + 279 z + 297 z^2 - 3080 z^3 + 1848 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 12 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (12 - 231 z^2 + 154 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-48 + 27 z - 495 z^2 + 308 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-384 + 279 z + 297 z^2 - 3080 z^3 + 1848 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

 Standard Form

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 MathML Form

 2 F 1 ( - 9 8 , 21 8 ; 4 ; z ) 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["9", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["21", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["4", 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] 1 2734875 π z 3 ( 1024 2 3 / 4 1 - z + 1 4 ( - 4 ( 1848 z 4 - 3080 z 3 + 297 z 2 + 279 z - 384 ) E ( 1 2 - 1 2 1 - z + 1 ) - 12 2 1 - z + 1 1 - z ( 154 z 3 - 231 z 2 + 12 ) K ( 1 2 - 1 2 1 - z + 1 ) + 5 2 1 - z + 1 ( 308 z 3 - 495 z 2 + 27 z - 48 ) K ( 1 2 - 1 2 1 - z + 1 ) + 2 ( 1848 z 4 - 3080 z 3 + 297 z 2 + 279 z - 384 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ -1 9 8 21 8 4 z 1 2734875 z 3 -1 1024 2 3 4 1 -1 z 1 2 1 1 4 -4 1848 z 4 -1 3080 z 3 297 z 2 279 z -384 EllipticE 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 12 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 2 154 z 3 -1 231 z 2 12 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 5 2 1 2 1 -1 z 1 2 1 1 2 308 z 3 -1 495 z 2 27 z -48 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 2 1848 z 4 -1 3080 z 3 297 z 2 279 z -384 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02