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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.a989.01

 Input Form

 Hypergeometric2F1[-(19/4), -(3/2), 1, z] == (1/(21945 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]])) (2 (1 - z)^(1/4) (118772 + 429945 z + 37584 z^2 - 6896 z^3 + 720 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (118772 + 429945 z + 37584 z^2 - 6896 z^3 + 720 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (118772 + 429945 z + 37584 z^2 - 6896 z^3 + 720 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (118772 + 429945 z + 37584 z^2 - 6896 z^3 + 720 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (118772 + 429945 z + 37584 z^2 - 6896 z^3 + 720 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-30992 + 243901 z + 399744 z^2 - 38848 z^3 + 7040 z^4 - 720 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])

 Standard Form

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 MathML Form

 2 F 1 ( - 19 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["19", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", 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 21945 2 π 1 - z + 1 ( 2 ( 1 - z ) 3 / 4 ( 720 z 4 - 6896 z 3 + 37584 z 2 + 429945 z + 118772 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 2 1 - z 4 ( 720 z 4 - 6896 z 3 + 37584 z 2 + 429945 z + 118772 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( 1 - z ) 3 / 4 ( 720 z 4 - 6896 z 3 + 37584 z 2 + 429945 z + 118772 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 1 - z ( 720 z 4 - 6896 z 3 + 37584 z 2 + 429945 z + 118772 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 1 - z 4 ( 720 z 4 - 6896 z 3 + 37584 z 2 + 429945 z + 118772 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( - 720 z 5 + 7040 z 4 - 38848 z 3 + 399744 z 2 + 243901 z - 30992 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) HypergeometricPFQ -1 19 4 -1 3 2 1 z 1 21945 2 1 2 1 -1 z 1 2 1 1 2 -1 2 1 -1 z 3 4 720 z 4 -1 6896 z 3 37584 z 2 429945 z 118772 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 2 1 -1 z 1 4 720 z 4 -1 6896 z 3 37584 z 2 429945 z 118772 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 3 4 720 z 4 -1 6896 z 3 37584 z 2 429945 z 118772 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 1 2 720 z 4 -1 6896 z 3 37584 z 2 429945 z 118772 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 1 4 720 z 4 -1 6896 z 3 37584 z 2 429945 z 118772 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -720 z 5 7040 z 4 -1 38848 z 3 399744 z 2 243901 z -30992 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