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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[11/4, 7/2, 6, z] == (1/(945 Pi Sqrt[1 + Sqrt[1 - z]] z^5)) (2048 Sqrt[2] (-2 (512 - 368 z + 21 z^2) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (512 - 368 z + 21 z^2) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (512 - 368 z + 21 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (512 - 368 z + 21 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (512 - 368 z + 21 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + ((512 - 624 z + 157 z^2) EllipticK[1/2 - (1 - z)^(1/4)/ (1 + Sqrt[1 - z])])/(1 - z)^(1/4)))

 Standard Form

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 MathML Form

 2 F 1 ( 11 4 , 7 2 ; 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["11", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "2"], 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] 1 945 π 1 - z + 1 z 5 ( 2048 2 ( - 2 1 - z ( 21 z 2 - 368 z + 512 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) - 2 ( 21 z 2 - 368 z + 512 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z ( 21 z 2 - 368 z + 512 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z 4 ( 21 z 2 - 368 z + 512 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 21 z 2 - 368 z + 512 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 157 z 2 - 624 z + 512 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) 1 - z 4 ) ) HypergeometricPFQ 11 4 7 2 6 z 1 945 1 -1 z 1 2 1 1 2 z 5 -1 2048 2 1 2 -2 1 -1 z 1 2 21 z 2 -1 368 z 512 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 2 21 z 2 -1 368 z 512 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 2 21 z 2 -1 368 z 512 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 4 21 z 2 -1 368 z 512 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 21 z 2 -1 368 z 512 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 157 z 2 -1 624 z 512 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 4 -1 [/itex]

 Rule Form

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

 2007-05-02