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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[21/4, 11/2, 3, z] == (2 Sqrt[2] (2 (1 - z)^(1/4) (-160 + 3040 z + 118912 z^2 + 157484 z^3 + 23565 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-160 + 3040 z + 118912 z^2 + 157484 z^3 + 23565 z^4) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-1 + z) (-160 + 2960 z + 50752 z^2 + 44080 z^3 + 3315 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-160 + 3040 z + 118912 z^2 + 157484 z^3 + 23565 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-160 + 3040 z + 118912 z^2 + 157484 z^3 + 23565 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-160 + 3040 z + 118912 z^2 + 157484 z^3 + 23565 z^4) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (69615 Pi Sqrt[1 + Sqrt[1 - z]] (-1 + z)^8 z^2)

 Standard Form

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 MathML Form

 2 F 1 ( 21 4 , 11 2 ; 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["21", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "2"], 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 2 ( 2 ( 1 - z ) 3 / 4 ( 23565 z 4 + 157484 z 3 + 118912 z 2 + 3040 z - 160 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + 2 1 - z 4 ( 23565 z 4 + 157484 z 3 + 118912 z 2 + 3040 z - 160 ) E ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) + ( z - 1 ) ( 3315 z 4 + 44080 z 3 + 50752 z 2 + 2960 z - 160 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - ( 1 - z ) 3 / 4 ( 23565 z 4 + 157484 z 3 + 118912 z 2 + 3040 z - 160 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 1 - z ( 23565 z 4 + 157484 z 3 + 118912 z 2 + 3040 z - 160 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) - 1 - z 4 ( 23565 z 4 + 157484 z 3 + 118912 z 2 + 3040 z - 160 ) K ( 2 1 - z 4 ( 1 - z - 1 ) + z 2 z ) ) ) / ( 69615 π 1 - z + 1 ( z - 1 ) 8 z 2 ) HypergeometricPFQ 21 4 11 2 3 z 2 2 1 2 2 1 -1 z 3 4 23565 z 4 157484 z 3 118912 z 2 3040 z -160 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 2 1 -1 z 1 4 23565 z 4 157484 z 3 118912 z 2 3040 z -160 EllipticE 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 z -1 3315 z 4 44080 z 3 50752 z 2 2960 z -160 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 3 4 23565 z 4 157484 z 3 118912 z 2 3040 z -160 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 1 2 23565 z 4 157484 z 3 118912 z 2 3040 z -160 EllipticK 2 1 -1 z 1 4 1 -1 z 1 2 -1 z 2 z -1 -1 1 -1 z 1 4 23565 z 4 157484 z 3 118912 z 2 3040 z -160 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 8 z 2 -1 [/itex]

 Rule Form

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

 2007-05-02