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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ak9x.01

 Input Form

 Hypergeometric2F1[3/2, 15/4, 1, z] == (Sqrt[2] (2 (1 - z)^(3/2) (-493 - 112 z + 20 z^2) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 (-1 + z) (-493 - 112 z + 20 z^2) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(5/4) (-493 - 112 z + 20 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/2) (-493 - 112 z + 20 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-1 + z) (-493 - 112 z + 20 z^2) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (31 - 712 z + 116 z^2 - 20 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (231 Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^5)

 Standard Form

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 MathML Form

 2 F 1 ( 3 2 , 15 4 ; 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["15", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["1", 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] 1 231 π 1 - z + 1 ( z - 1 ) 5 ( 2 ( 2 ( 20 z 2 - 112 z - 493 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 2 - ( 20 z 2 - 112 z - 493 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 2 - ( 20 z 2 - 112 z - 493 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 5 / 4 + ( - 20 z 3 + 116 z 2 - 712 z + 31 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 4 - 2 ( z - 1 ) ( 20 z 2 - 112 z - 493 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + ( z - 1 ) ( 20 z 2 - 112 z - 493 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ 3 2 15 4 1 z 1 231 1 -1 z 1 2 1 1 2 z -1 5 -1 2 1 2 2 20 z 2 -1 112 z -493 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 2 -1 20 z 2 -1 112 z -493 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 2 -1 20 z 2 -1 112 z -493 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 5 4 -20 z 3 116 z 2 -1 712 z 31 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 4 -1 2 z -1 20 z 2 -1 112 z -493 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 z -1 20 z 2 -1 112 z -493 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 [/itex]

 Rule Form

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

 2007-05-02