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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.a94r.01

 Input Form

 Hypergeometric2F1[-(19/4), -(11/4), -(5/2), z] == (1/(200 Pi^(3/2))) ((2 Sqrt[z] (100 - 485 z + 970 z^2 + 1771 z^3 - 308 z^4) EllipticE[(1/2) (1 - Sqrt[z])] + 2 Sqrt[z] (-100 + 485 z - 970 z^2 - 1771 z^3 + 308 z^4) EllipticE[(1/2) (1 + Sqrt[z])] + (200 - 100 Sqrt[z] - 1120 z + 485 z^(3/2) + 2645 z^2 - 970 z^(5/2) - 3850 z^3 - 1771 z^(7/2) + 77 z^4 + 308 z^(9/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (200 + 100 Sqrt[z] - 1120 z - 485 z^(3/2) + 2645 z^2 + 970 z^(5/2) - 3850 z^3 + 1771 z^(7/2) + 77 z^4 - 308 z^(9/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

 Standard Form

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 MathML Form

 2 F 1 ( - 19 4 , - 11 4 ; - 5 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["19", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", 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[RowBox[List["-", FractionBox["5", "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] 1 200 π 3 / 2 ( ( 2 z ( - 308 z 4 + 1771 z 3 + 970 z 2 - 485 z + 100 ) E ( 1 2 ( 1 - z ) ) + 2 z ( 308 z 4 - 1771 z 3 - 970 z 2 + 485 z - 100 ) E ( 1 2 ( z + 1 ) ) + ( 308 z 9 / 2 + 77 z 4 - 1771 z 7 / 2 - 3850 z 3 - 970 z 5 / 2 + 2645 z 2 + 485 z 3 / 2 - 1120 z - 100 z + 200 ) K ( 1 2 ( 1 - z ) ) + ( - 308 z 9 / 2 + 77 z 4 + 1771 z 7 / 2 - 3850 z 3 + 970 z 5 / 2 + 2645 z 2 - 485 z 3 / 2 - 1120 z + 100 z + 200 ) K ( 1 2 ( z + 1 ) ) ) Γ ( 3 4 ) 2 ) HypergeometricPFQ -1 19 4 -1 11 4 -1 5 2 z 1 200 3 2 -1 2 z 1 2 -308 z 4 1771 z 3 970 z 2 -1 485 z 100 EllipticE 1 2 1 -1 z 1 2 2 z 1 2 308 z 4 -1 1771 z 3 -1 970 z 2 485 z -100 EllipticE 1 2 z 1 2 1 308 z 9 2 77 z 4 -1 1771 z 7 2 -1 3850 z 3 -1 970 z 5 2 2645 z 2 485 z 3 2 -1 1120 z -1 100 z 1 2 200 EllipticK 1 2 1 -1 z 1 2 -308 z 9 2 77 z 4 1771 z 7 2 -1 3850 z 3 970 z 5 2 2645 z 2 -1 485 z 3 2 -1 1120 z 100 z 1 2 200 EllipticK 1 2 z 1 2 1 Gamma 3 4 2 [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2007-05-02