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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/2, 9/4, 6, z] == (1/(24255 Pi Sqrt[1 + Sqrt[1 - z]] z^5)) (512 Sqrt[2] (-2 (1 - z)^(1/4) (-2048 + 5568 z - 4596 z^2 + 770 z^3 + 231 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (-2048 + 5568 z - 4596 z^2 + 770 z^3 + 231 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-2048 + 6592 z - 7188 z^2 + 2642 z^3 + 77 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-2048 + 5568 z - 4596 z^2 + 770 z^3 + 231 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-2048 + 5568 z - 4596 z^2 + 770 z^3 + 231 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-2048 + 5568 z - 4596 z^2 + 770 z^3 + 231 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))

 Standard Form

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 MathML Form

 2 F 1 ( 1 2 , 9 4 ; 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["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "4"], 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 24255 π 1 - z + 1 z 5 ( 512 2 ( - 2 ( 1 - z ) 3 / 4 ( 231 z 4 + 770 z 3 - 4596 z 2 + 5568 z - 2048 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 2 1 - z 4 ( 231 z 4 + 770 z 3 - 4596 z 2 + 5568 z - 2048 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( 77 z 4 + 2642 z 3 - 7188 z 2 + 6592 z - 2048 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( 1 - z ) 3 / 4 ( 231 z 4 + 770 z 3 - 4596 z 2 + 5568 z - 2048 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 1 - z ( 231 z 4 + 770 z 3 - 4596 z 2 + 5568 z - 2048 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 1 - z 4 ( 231 z 4 + 770 z 3 - 4596 z 2 + 5568 z - 2048 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) HypergeometricPFQ 1 2 9 4 6 z 1 24255 1 -1 z 1 2 1 1 2 z 5 -1 512 2 1 2 -2 1 -1 z 3 4 231 z 4 770 z 3 -1 4596 z 2 5568 z -2048 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 2 1 -1 z 1 4 231 z 4 770 z 3 -1 4596 z 2 5568 z -2048 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 77 z 4 2642 z 3 -1 7188 z 2 6592 z -2048 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 3 4 231 z 4 770 z 3 -1 4596 z 2 5568 z -2048 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 2 231 z 4 770 z 3 -1 4596 z 2 5568 z -2048 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 4 231 z 4 770 z 3 -1 4596 z 2 5568 z -2048 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 [/itex]

 Rule Form

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

 2007-05-02