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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[9/2, 21/4, 3, z] == (4 Sqrt[2] (-2 (1 - z)^(1/4) (-144 + 2124 z + 56048 z^2 + 41575 z^3 + 1344 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (-144 + 2124 z + 56048 z^2 + 41575 z^3 + 1344 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (-1 + z) (-144 + 2052 z + 22244 z^2 + 9497 z^3) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-144 + 2124 z + 56048 z^2 + 41575 z^3 + 1344 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-144 + 2124 z + 56048 z^2 + 41575 z^3 + 1344 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-144 + 2124 z + 56048 z^2 + 41575 z^3 + 1344 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (69615 Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^7 z^2)

 Standard Form

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 MathML Form

 2 F 1 ( 9 2 , 21 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[FractionBox["9", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["21", "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] ( 4 2 ( - 2 ( 1 - z ) 3 / 4 ( 1344 z 4 + 41575 z 3 + 56048 z 2 + 2124 z - 144 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 2 1 - z 4 ( 1344 z 4 + 41575 z 3 + 56048 z 2 + 2124 z - 144 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( z - 1 ) ( 9497 z 3 + 22244 z 2 + 2052 z - 144 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( 1 - z ) 3 / 4 ( 1344 z 4 + 41575 z 3 + 56048 z 2 + 2124 z - 144 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 1 - z ( 1344 z 4 + 41575 z 3 + 56048 z 2 + 2124 z - 144 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 1 - z 4 ( 1344 z 4 + 41575 z 3 + 56048 z 2 + 2124 z - 144 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) / ( 69615 π 1 - z + 1 ( z - 1 ) 7 z 2 ) HypergeometricPFQ 9 2 21 4 3 z 4 2 1 2 -2 1 -1 z 3 4 1344 z 4 41575 z 3 56048 z 2 2124 z -144 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 2 1 -1 z 1 4 1344 z 4 41575 z 3 56048 z 2 2124 z -144 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 z -1 9497 z 3 22244 z 2 2052 z -144 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 3 4 1344 z 4 41575 z 3 56048 z 2 2124 z -144 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 2 1344 z 4 41575 z 3 56048 z 2 2124 z -144 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 4 1344 z 4 41575 z 3 56048 z 2 2124 z -144 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 69615 1 -1 z 1 2 1 1 2 z -1 7 z 2 -1 [/itex]

 Rule Form

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

 2007-05-02