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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(9/8), 37/8, 3, z] == (1/(10094175 Pi z^2)) (128 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-8 (156 + 1287 z - 50512 z^2 + 70224 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (39 - 15444 z + 23408 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1/Sqrt[1 - z]) (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (39 + 26598 z - 72688 z^2 + 46816 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) + 4 (156 + 1287 z - 50512 z^2 + 70224 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

 Standard Form

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 MathML Form

 2 F 1 ( - 9 8 , 37 8 ; 3 ; 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["37", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["3", 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 10094175 π z 2 ( 128 2 3 / 4 1 - z + 1 4 ( - 8 ( 70224 z 3 - 50512 z 2 + 1287 z + 156 ) E ( 1 2 - 1 2 1 - z + 1 ) + 5 2 1 - z + 1 ( 23408 z 2 - 15444 z + 39 ) K ( 1 2 - 1 2 1 - z + 1 ) + 3 2 1 - z + 1 ( 46816 z 3 - 72688 z 2 + 26598 z + 39 ) K ( 1 2 - 1 2 1 - z + 1 ) 1 - z + 4 ( 70224 z 3 - 50512 z 2 + 1287 z + 156 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ -1 9 8 37 8 3 z 1 10094175 z 2 -1 128 2 3 4 1 -1 z 1 2 1 1 4 -8 70224 z 3 -1 50512 z 2 1287 z 156 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 23408 z 2 -1 15444 z 39 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 3 2 1 2 1 -1 z 1 2 1 1 2 46816 z 3 -1 72688 z 2 26598 z 39 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 1 -1 z 1 2 -1 4 70224 z 3 -1 50512 z 2 1287 z 156 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