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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.al7y.01

 Input Form

 Hypergeometric2F1[9/4, 7/2, 6, z] == -((1/(1155 Pi Sqrt[1 + Sqrt[1 - z]] z^5)) (2048 Sqrt[2] (2 (1 + Sqrt[1 - z]) (1 - z)^(1/4) (512 - 336 z + 5 z^2) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (512 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) - 16 (37 + 21 (1 - z)^(1/4) + 21 Sqrt[1 - z] + 21 (1 - z)^(3/4)) z + 5 (25 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) z^2 + 5 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])))

 Standard Form

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 MathML Form

 2 F 1 ( 9 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["9", "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 1155 π 1 - z + 1 z 5 ( 2048 2 ( 2 ( 1 - z + 1 ) 1 - z 4 ( 5 z 2 - 336 z + 512 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( 5 z 3 + 5 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 25 ) z 2 - 16 ( 21 ( 1 - z ) 3 / 4 + 21 1 - z + 21 1 - z 4 + 37 ) z + 512 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 1 ) ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) HypergeometricPFQ 9 4 7 2 6 z -1 1 1155 1 -1 z 1 2 1 1 2 z 5 -1 2048 2 1 2 2 1 -1 z 1 2 1 1 -1 z 1 4 5 z 2 -1 336 z 512 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 5 z 3 5 1 -1 z 3 4 1 -1 z 1 2 1 -1 z 1 4 25 z 2 -1 16 21 1 -1 z 3 4 21 1 -1 z 1 2 21 1 -1 z 1 4 37 z 512 1 -1 z 3 4 1 -1 z 1 2 1 -1 z 1 4 1 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