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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ac25.01

 Input Form

 Hypergeometric2F1[-(7/2), 11/4, 1, z] == (1/(140 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]])) (2 (736 - 4472 z + 7072 z^2 - 3315 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (736 - 4472 z + 7072 z^2 - 3315 z^3) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-736 + 4472 z - 7072 z^2 + 3315 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-736 + 4472 z - 7072 z^2 + 3315 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-736 + 4472 z - 7072 z^2 + 3315 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (176 + 936 z - 4420 z^2 + 3315 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])

 Standard Form

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 MathML Form

 2 F 1 ( - 7 2 , 11 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["7", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "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] 1 140 2 π 1 - z + 1 ( 2 1 - z ( - 3315 z 3 + 7072 z 2 - 4472 z + 736 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 2 ( - 3315 z 3 + 7072 z 2 - 4472 z + 736 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z ( 3315 z 3 - 7072 z 2 + 4472 z - 736 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z 4 ( 3315 z 3 - 7072 z 2 + 4472 z - 736 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 3315 z 3 - 7072 z 2 + 4472 z - 736 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - ( 1 - z ) 3 / 4 ( 3315 z 3 - 4420 z 2 + 936 z + 176 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) HypergeometricPFQ -1 7 2 11 4 1 z 1 140 2 1 2 1 -1 z 1 2 1 1 2 -1 2 1 -1 z 1 2 -3315 z 3 7072 z 2 -1 4472 z 736 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 2 -3315 z 3 7072 z 2 -1 4472 z 736 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 2 3315 z 3 -1 7072 z 2 4472 z -736 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 4 3315 z 3 -1 7072 z 2 4472 z -736 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 3315 z 3 -1 7072 z 2 4472 z -736 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 1 -1 z 3 4 3315 z 3 -1 4420 z 2 936 z 176 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