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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.btn0.01

 Input Form

 Hypergeometric2F1[-(7/8), 29/8, 2, z] == (16 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (13 - 184 z + 192 z^2) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (13 (1 + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + Sqrt[1 - z]) + (323 - 184 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) - 184 Sqrt[1 - z]) z + 48 (-23 + 4 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 4 Sqrt[1 - z]) z^2 + 768 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (4095 Pi (1 + Sqrt[1 - z])^(1/4) (-1 + z) z)

 Standard Form

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 MathML Form

 2 F 1 ( - 7 8 , 29 8 ; 2 ; 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["7", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["29", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[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] ( 16 2 4 ( 2 2 1 - z + 1 1 - z 4 ( 192 z 2 - 184 z + 13 ) E ( 1 2 - 1 - z 4 2 1 - z + 1 ) - ( 768 z 3 + 48 ( 4 2 1 - z 4 1 - z + 1 + 4 1 - z - 23 ) z 2 + ( - 184 2 1 - z 4 1 - z + 1 - 184 1 - z + 323 ) z + 13 ( 2 1 - z 4 1 - z + 1 + 1 - z + 1 ) ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) ) ) / ( 4095 π 1 - z + 1 4 ( z - 1 ) z ) HypergeometricPFQ -1 7 8 29 8 2 z 16 2 1 4 2 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 4 192 z 2 -1 184 z 13 EllipticE 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 768 z 3 48 4 2 1 2 1 -1 z 1 4 1 -1 z 1 2 1 1 2 4 1 -1 z 1 2 -23 z 2 -184 2 1 2 1 -1 z 1 4 1 -1 z 1 2 1 1 2 -1 184 1 -1 z 1 2 323 z 13 2 1 2 1 -1 z 1 4 1 -1 z 1 2 1 1 2 1 -1 z 1 2 1 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 4095 1 -1 z 1 2 1 1 4 z -1 z -1 [/itex]

 Rule Form

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

 2007-05-02