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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.a840.01

 Input Form

 Hypergeometric2F1[-(11/2), 21/4, 1, z] == (2 (1 - z)^(1/4) (38977856 - 878076336 z + 5114599056 z^2 - 11833141936 z^3 + 11828969460 z^4 - 4271572305 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (38977856 - 878076336 z + 5114599056 z^2 - 11833141936 z^3 + 11828969460 z^4 - 4271572305 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-22641536 + 423811984 z - 2175001440 z^2 + 4563930112 z^3 - 4214200760 z^4 + 1423857435 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-38977856 + 878076336 z - 5114599056 z^2 + 11833141936 z^3 - 11828969460 z^4 + 4271572305 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-38977856 + 878076336 z - 5114599056 z^2 + 11833141936 z^3 - 11828969460 z^4 + 4271572305 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-38977856 + 878076336 z - 5114599056 z^2 + 11833141936 z^3 - 11828969460 z^4 + 4271572305 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (4084080 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]])

 Standard Form

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 MathML Form

 2 F 1 ( - 11 2 , 21 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["11", "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["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] ( 2 ( 1 - z ) 3 / 4 ( - 4271572305 z 5 + 11828969460 z 4 - 11833141936 z 3 + 5114599056 z 2 - 878076336 z + 38977856 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 2 1 - z 4 ( - 4271572305 z 5 + 11828969460 z 4 - 11833141936 z 3 + 5114599056 z 2 - 878076336 z + 38977856 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( 1423857435 z 5 - 4214200760 z 4 + 4563930112 z 3 - 2175001440 z 2 + 423811984 z - 22641536 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( 1 - z ) 3 / 4 ( 4271572305 z 5 - 11828969460 z 4 + 11833141936 z 3 - 5114599056 z 2 + 878076336 z - 38977856 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 1 - z ( 4271572305 z 5 - 11828969460 z 4 + 11833141936 z 3 - 5114599056 z 2 + 878076336 z - 38977856 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 1 - z 4 ( 4271572305 z 5 - 11828969460 z 4 + 11833141936 z 3 - 5114599056 z 2 + 878076336 z - 38977856 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) / ( 4084080 2 π 1 - z + 1 ) HypergeometricPFQ -1 11 2 21 4 1 z 2 1 -1 z 3 4 -4271572305 z 5 11828969460 z 4 -1 11833141936 z 3 5114599056 z 2 -1 878076336 z 38977856 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 2 1 -1 z 1 4 -4271572305 z 5 11828969460 z 4 -1 11833141936 z 3 5114599056 z 2 -1 878076336 z 38977856 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1423857435 z 5 -1 4214200760 z 4 4563930112 z 3 -1 2175001440 z 2 423811984 z -22641536 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 3 4 4271572305 z 5 -1 11828969460 z 4 11833141936 z 3 -1 5114599056 z 2 878076336 z -38977856 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 2 4271572305 z 5 -1 11828969460 z 4 11833141936 z 3 -1 5114599056 z 2 878076336 z -38977856 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 1 -1 z 1 4 4271572305 z 5 -1 11828969460 z 4 11833141936 z 3 -1 5114599056 z 2 878076336 z -38977856 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 4084080 2 1 2 1 -1 z 1 2 1 1 2 -1 [/itex]

 Rule Form

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

 2007-05-02