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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.abc0.01

 Input Form

 Hypergeometric2F1[-(15/4), 1/2, 2, z] == (1/(7315 Pi Sqrt[1 + Sqrt[1 - z]] z)) (4 Sqrt[2] (-2 (1 - z)^(1/4) (-385 - 1548 z + 1352 z^2 - 654 z^3 + 130 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (-385 - 1548 z + 1352 z^2 - 654 z^3 + 130 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-385 - 1548 z + 1352 z^2 - 654 z^3 + 130 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-385 - 1548 z + 1352 z^2 - 654 z^3 + 130 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-385 - 1548 z + 1352 z^2 - 654 z^3 + 130 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-385 + 2302 z - 1724 z^2 + 1462 z^3 - 680 z^4 + 130 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 ( - 15 4 , 1 2 ; 2 ; 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["1", "2"], 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] 1 7315 π 1 - z + 1 z ( 4 2 ( - 2 ( 1 - z ) 3 / 4 ( 130 z 4 - 654 z 3 + 1352 z 2 - 1548 z - 385 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 2 1 - z 4 ( 130 z 4 - 654 z 3 + 1352 z 2 - 1548 z - 385 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( 1 - z ) 3 / 4 ( 130 z 4 - 654 z 3 + 1352 z 2 - 1548 z - 385 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 1 - z ( 130 z 4 - 654 z 3 + 1352 z 2 - 1548 z - 385 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 1 - z 4 ( 130 z 4 - 654 z 3 + 1352 z 2 - 1548 z - 385 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( 130 z 5 - 680 z 4 + 1462 z 3 - 1724 z 2 + 2302 z - 385 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) HypergeometricPFQ -1 15 4 1 2 2 z 1 7315 1 -1 z 1 2 1 1 2 z -1 4 2 1 2 -2 1 -1 z 3 4 130 z 4 -1 654 z 3 1352 z 2 -1 1548 z -385 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 2 1 -1 z 1 4 130 z 4 -1 654 z 3 1352 z 2 -1 1548 z -385 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 3 4 130 z 4 -1 654 z 3 1352 z 2 -1 1548 z -385 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 2 130 z 4 -1 654 z 3 1352 z 2 -1 1548 z -385 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 4 130 z 4 -1 654 z 3 1352 z 2 -1 1548 z -385 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 130 z 5 -1 680 z 4 1462 z 3 -1 1724 z 2 2302 z -385 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