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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.aa6r.01

 Input Form

 Hypergeometric2F1[-(9/2), 23/4, 3, z] == (2 (-2688 - 65856 z + 4117040 z^2 - 25298720 z^3 + 56142840 z^4 - 52681980 z^5 + 17784975 z^6) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-2688 - 65856 z + 4117040 z^2 - 25298720 z^3 + 56142840 z^4 - 52681980 z^5 + 17784975 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (2688 + 65856 z - 4117040 z^2 + 25298720 z^3 - 56142840 z^4 + 52681980 z^5 - 17784975 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (2688 + 65856 z - 4117040 z^2 + 25298720 z^3 - 56142840 z^4 + 52681980 z^5 - 17784975 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (2688 + 65856 z - 4117040 z^2 + 25298720 z^3 - 56142840 z^4 + 52681980 z^5 - 17784975 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (2688 + 67200 z - 659600 z^2 - 4119440 z^3 + 25379640 z^4 - 38454000 z^5 + 17784975 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (855855 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^2)

 Standard Form

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 MathML Form

 2 F 1 ( - 9 2 , 23 4 ; 3 ; 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", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["23", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["3", 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] ( 2 1 - z ( 17784975 z 6 - 52681980 z 5 + 56142840 z 4 - 25298720 z 3 + 4117040 z 2 - 65856 z - 2688 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 2 ( 17784975 z 6 - 52681980 z 5 + 56142840 z 4 - 25298720 z 3 + 4117040 z 2 - 65856 z - 2688 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z ( - 17784975 z 6 + 52681980 z 5 - 56142840 z 4 + 25298720 z 3 - 4117040 z 2 + 65856 z + 2688 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z 4 ( - 17784975 z 6 + 52681980 z 5 - 56142840 z 4 + 25298720 z 3 - 4117040 z 2 + 65856 z + 2688 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + ( - 17784975 z 6 + 52681980 z 5 - 56142840 z 4 + 25298720 z 3 - 4117040 z 2 + 65856 z + 2688 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 1 - z ) 3 / 4 ( 17784975 z 6 - 38454000 z 5 + 25379640 z 4 - 4119440 z 3 - 659600 z 2 + 67200 z + 2688 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) / ( 855855 2 π 1 - z + 1 z 2 ) HypergeometricPFQ -1 9 2 23 4 3 z 2 1 -1 z 1 2 17784975 z 6 -1 52681980 z 5 56142840 z 4 -1 25298720 z 3 4117040 z 2 -1 65856 z -2688 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 2 17784975 z 6 -1 52681980 z 5 56142840 z 4 -1 25298720 z 3 4117040 z 2 -1 65856 z -2688 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 2 -17784975 z 6 52681980 z 5 -1 56142840 z 4 25298720 z 3 -1 4117040 z 2 65856 z 2688 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 4 -17784975 z 6 52681980 z 5 -1 56142840 z 4 25298720 z 3 -1 4117040 z 2 65856 z 2688 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -17784975 z 6 52681980 z 5 -1 56142840 z 4 25298720 z 3 -1 4117040 z 2 65856 z 2688 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 4 17784975 z 6 -1 38454000 z 5 25379640 z 4 -1 4119440 z 3 -1 659600 z 2 67200 z 2688 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 855855 2 1 2 1 -1 z 1 2 1 1 2 z 2 -1 [/itex]

 Rule Form

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

 2007-05-02