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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(9/4), 7/2, 2, z] == (1/(585 Pi Sqrt[1 + Sqrt[1 - z]] z)) (Sqrt[2] (2 (1 + Sqrt[1 - z]) (-36 + 2134 z - 6391 z^2 + 4389 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (36 (1 + (1 - z)^(1/4) + Sqrt[1 - z] + (1 - z)^(3/4)) - 22 (97 + 97 (1 - z)^(1/4) + 97 Sqrt[1 - z] + 43 (1 - z)^(3/4)) z + 77 (83 + 83 (1 - z)^(1/4) + 83 Sqrt[1 - z] + 19 (1 - z)^(3/4)) z^2 - 4389 (1 + (1 - z)^(1/4) + Sqrt[1 - z]) z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))

 Standard Form

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 MathML Form

 2 F 1 ( - 9 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["9", "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] 1 585 π 1 - z + 1 z ( 2 ( 2 ( 1 - z + 1 ) ( 4389 z 3 - 6391 z 2 + 2134 z - 36 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + ( - 4389 ( 1 - z + 1 - z 4 + 1 ) z 3 + 77 ( 19 ( 1 - z ) 3 / 4 + 83 1 - z + 83 1 - z 4 + 83 ) z 2 - 22 ( 43 ( 1 - z ) 3 / 4 + 97 1 - z + 97 1 - z 4 + 97 ) z + 36 ( ( 1 - z ) 3 / 4 + 1 - z + 1 - z 4 + 1 ) ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ -1 9 4 7 2 2 z 1 585 1 -1 z 1 2 1 1 2 z -1 2 1 2 2 1 -1 z 1 2 1 4389 z 3 -1 6391 z 2 2134 z -36 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -4389 1 -1 z 1 2 1 -1 z 1 4 1 z 3 77 19 1 -1 z 3 4 83 1 -1 z 1 2 83 1 -1 z 1 4 83 z 2 -1 22 43 1 -1 z 3 4 97 1 -1 z 1 2 97 1 -1 z 1 4 97 z 36 1 -1 z 3 4 1 -1 z 1 2 1 -1 z 1 4 1 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