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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ag62.01

 Input Form

 Hypergeometric2F1[-(5/4), 7/2, 2, z] == (1/(45 Pi Sqrt[1 + Sqrt[1 - z]] z)) (Sqrt[2] (-2 (4 - 154 z + 231 z^2) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (4 - 154 z + 231 z^2) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + ((4 - 66 z + 77 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (1 - z)^(1/4) + (4 - 154 z + 231 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (4 - 154 z + 231 z^2) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (4 - 154 z + 231 z^2) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))

 Standard Form

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 MathML Form

 2 F 1 ( - 5 4 , 7 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["5", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "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 45 π 1 - z + 1 z ( 2 ( - 2 1 - z ( 231 z 2 - 154 z + 4 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) - 2 ( 231 z 2 - 154 z + 4 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 77 z 2 - 66 z + 4 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) 1 - z 4 + 1 - z ( 231 z 2 - 154 z + 4 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z 4 ( 231 z 2 - 154 z + 4 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 231 z 2 - 154 z + 4 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ -1 5 4 7 2 2 z 1 45 1 -1 z 1 2 1 1 2 z -1 2 1 2 -2 1 -1 z 1 2 231 z 2 -1 154 z 4 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 2 231 z 2 -1 154 z 4 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 77 z 2 -1 66 z 4 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 4 -1 1 -1 z 1 2 231 z 2 -1 154 z 4 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 4 231 z 2 -1 154 z 4 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 231 z 2 -1 154 z 4 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