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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(1/2), 19/4, 1, z] == (Sqrt[2] (-2 (1 - z)^(3/2) (-873 + 2947 z - 3159 z^2 + 1105 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 (-1 + z) (-873 + 2947 z - 3159 z^2 + 1105 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(5/4) (873 - 2947 z + 3159 z^2 - 1105 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/2) (873 - 2947 z + 3159 z^2 - 1105 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-1 + z) (873 - 2947 z + 3159 z^2 - 1105 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-103 - 1044 z + 3402 z^2 - 3380 z^3 + 1105 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (385 Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^4)

 Standard Form

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 MathML Form

 2 F 1 ( - 1 2 , 19 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[RowBox[List["-", FractionBox["1", "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["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 ( z - 1 ) 4 ( 2 ( - 2 ( 1105 z 3 - 3159 z 2 + 2947 z - 873 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 2 - ( - 1105 z 3 + 3159 z 2 - 2947 z + 873 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 2 - ( - 1105 z 3 + 3159 z 2 - 2947 z + 873 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 5 / 4 + ( 1105 z 4 - 3380 z 3 + 3402 z 2 - 1044 z - 103 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ( 1 - z ) 3 / 4 + 2 ( z - 1 ) ( 1105 z 3 - 3159 z 2 + 2947 z - 873 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + ( z - 1 ) ( - 1105 z 3 + 3159 z 2 - 2947 z + 873 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ -1 1 2 19 4 1 z 1 385 1 -1 z 1 2 1 1 2 z -1 4 -1 2 1 2 -2 1105 z 3 -1 3159 z 2 2947 z -873 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 2 -1 -1105 z 3 3159 z 2 -1 2947 z 873 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 2 -1 -1105 z 3 3159 z 2 -1 2947 z 873 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 5 4 1105 z 4 -1 3380 z 3 3402 z 2 -1 1044 z -103 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 4 2 z -1 1105 z 3 -1 3159 z 2 2947 z -873 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 z -1 -1105 z 3 3159 z 2 -1 2947 z 873 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