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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(1/4), 11/4, 6, -z] == (16384 Sqrt[2] ((-2048 - 5920 z - 5027 z^2 - 510 z^3 + 285 z^4 + 480 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (-2048 - 5920 z - 5027 z^2 - 510 z^3 + 285 z^4 + 480 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-2048 - 5408 z - 3915 z^2 - 15 z^3 + 120 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-2048 - 5920 z - 5027 z^2 - 510 z^3 + 285 z^4 + 480 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (4385745 Pi z^5 Sqrt[1 + Sqrt[1 + z]])

 Standard Form

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 MathML Form

 2 F 1 ( - 1 4 , 11 4 ; 6 ; - 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["1", "4"]]], 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["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "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 4385745 π z 5 z + 1 + 1 ( 16384 2 ( z + 1 ( 480 z 5 + 285 z 4 - 510 z 3 - 5027 z 2 - 5920 z - 2048 ) E ( z + 1 - 1 z + 1 + 1 ) + ( 480 z 5 + 285 z 4 - 510 z 3 - 5027 z 2 - 5920 z - 2048 ) E ( z + 1 - 1 z + 1 + 1 ) - z + 1 ( 120 z 4 - 15 z 3 - 3915 z 2 - 5408 z - 2048 ) K ( z + 1 - 1 z + 1 + 1 ) - ( 480 z 5 + 285 z 4 - 510 z 3 - 5027 z 2 - 5920 z - 2048 ) K ( z + 1 - 1 z + 1 + 1 ) ) ) HypergeometricPFQ -1 1 4 11 4 6 -1 z 1 4385745 z 5 z 1 1 2 1 1 2 -1 16384 2 1 2 z 1 1 2 480 z 5 285 z 4 -1 510 z 3 -1 5027 z 2 -1 5920 z -2048 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 480 z 5 285 z 4 -1 510 z 3 -1 5027 z 2 -1 5920 z -2048 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 -1 z 1 1 2 120 z 4 -1 15 z 3 -1 3915 z 2 -1 5408 z -2048 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 -1 480 z 5 285 z 4 -1 510 z 3 -1 5027 z 2 -1 5920 z -2048 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 [/itex]

 Rule Form

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

 2007-05-02