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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[3/2, 19/4, 2, z] == (4 Sqrt[2] (-2 (1 - z)^(3/2) (77 + 212 z - 124 z^2 + 30 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 (-1 + z) (77 + 212 z - 124 z^2 + 30 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(5/4) (77 + 212 z - 124 z^2 + 30 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/2) (77 + 212 z - 124 z^2 + 30 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-1 + z) (77 + 212 z - 124 z^2 + 30 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (77 - 404 z + 232 z^2 - 130 z^3 + 30 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (1155 Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^5 z)

 Standard Form

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 MathML Form

 2 F 1 ( 3 2 , 19 4 ; 2 ; 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["19", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["2", 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] ( 4 2 ( - 2 ( 30 z 3 - 124 z 2 + 212 z + 77 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 2 + ( 30 z 3 - 124 z 2 + 212 z + 77 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 2 + ( 30 z 3 - 124 z 2 + 212 z + 77 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 5 / 4 + ( 30 z 4 - 130 z 3 + 232 z 2 - 404 z + 77 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 4 + 2 ( z - 1 ) ( 30 z 3 - 124 z 2 + 212 z + 77 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) - ( z - 1 ) ( 30 z 3 - 124 z 2 + 212 z + 77 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) / ( 1155 π 1 - z + 1 ( z - 1 ) 5 z ) HypergeometricPFQ 3 2 19 4 2 z 4 2 1 2 -2 30 z 3 -1 124 z 2 212 z 77 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 2 30 z 3 -1 124 z 2 212 z 77 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 2 30 z 3 -1 124 z 2 212 z 77 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 5 4 30 z 4 -1 130 z 3 232 z 2 -1 404 z 77 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 4 2 z -1 30 z 3 -1 124 z 2 212 z 77 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 z -1 30 z 3 -1 124 z 2 212 z 77 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1155 1 -1 z 1 2 1 1 2 z -1 5 z -1 [/itex]

 Rule Form

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

 2007-05-02