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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.cb85.01

 Input Form

 Hypergeometric2F1[29/8, 47/8, 6, z] == (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (-1 + z) (-32768 + 86912 z - 66339 z^2 + 5005 z^3 + 4550 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (4096 - 10192 z + 6825 z^2 + 91 z^3 + 1820 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 6 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-2048 + 5992 z - 5369 z^2 + 910 z^3 + 2275 z^4) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (-1 + z) (-32768 + 86912 z - 66339 z^2 + 5005 z^3 + 4550 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (2922654735 Pi (-1 + z)^4 z^5)

 Standard Form

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 MathML Form

 2 F 1 ( 29 8 , 47 8 ; 6 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["29", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["47", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["6", 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 2922654735 π ( z - 1 ) 4 z 5 ( 262144 2 3 / 4 1 - z + 1 4 ( 4 ( z - 1 ) ( 4550 z 4 + 5005 z 3 - 66339 z 2 + 86912 z - 32768 ) E ( 1 2 - 1 2 1 - z + 1 ) + 5 2 1 - z + 1 ( z - 1 ) ( 1820 z 4 + 91 z 3 + 6825 z 2 - 10192 z + 4096 ) K ( 1 2 - 1 2 1 - z + 1 ) + 6 2 1 - z + 1 1 - z ( 2275 z 4 + 910 z 3 - 5369 z 2 + 5992 z - 2048 ) K ( 1 2 - 1 2 1 - z + 1 ) - 2 ( z - 1 ) ( 4550 z 4 + 5005 z 3 - 66339 z 2 + 86912 z - 32768 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ 29 8 47 8 6 z 1 2922654735 z -1 4 z 5 -1 262144 2 3 4 1 -1 z 1 2 1 1 4 4 z -1 4550 z 4 5005 z 3 -1 66339 z 2 86912 z -32768 EllipticE 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 z -1 1820 z 4 91 z 3 6825 z 2 -1 10192 z 4096 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 6 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 2 2275 z 4 910 z 3 -1 5369 z 2 5992 z -2048 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 2 z -1 4550 z 4 5005 z 3 -1 66339 z 2 86912 z -32768 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