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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(15/4), 3/2, 1, z] == (1/(385 Pi Sqrt[1 + Sqrt[1 - z]])) (Sqrt[2] (-2 (1 - z)^(1/4) (-873 + 2947 z - 3159 z^2 + 1105 z^3) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (-873 + 2947 z - 3159 z^2 + 1105 z^3) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-873 + 2947 z - 3159 z^2 + 1105 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-873 + 2947 z - 3159 z^2 + 1105 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-873 + 2947 z - 3159 z^2 + 1105 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-103 - 1044 z + 3402 z^2 - 3380 z^3 + 1105 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 ( - 15 4 , 3 2 ; 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["15", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "2"], 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] 1 385 π 1 - z + 1 ( 2 ( - 2 ( 1 - z ) 3 / 4 ( 1105 z 3 - 3159 z 2 + 2947 z - 873 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 2 1 - z 4 ( 1105 z 3 - 3159 z 2 + 2947 z - 873 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( 1 - z ) 3 / 4 ( 1105 z 3 - 3159 z 2 + 2947 z - 873 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 1 - z ( 1105 z 3 - 3159 z 2 + 2947 z - 873 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 1 - z 4 ( 1105 z 3 - 3159 z 2 + 2947 z - 873 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( 1105 z 4 - 3380 z 3 + 3402 z 2 - 1044 z - 103 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) HypergeometricPFQ -1 15 4 3 2 1 z 1 385 1 -1 z 1 2 1 1 2 -1 2 1 2 -2 1 -1 z 3 4 1105 z 3 -1 3159 z 2 2947 z -873 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 2 1 -1 z 1 4 1105 z 3 -1 3159 z 2 2947 z -873 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 3 4 1105 z 3 -1 3159 z 2 2947 z -873 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 2 1105 z 3 -1 3159 z 2 2947 z -873 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 4 1105 z 3 -1 3159 z 2 2947 z -873 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1105 z 4 -1 3380 z 3 3402 z 2 -1 1044 z -103 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