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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c4tn.01

 Input Form

 Hypergeometric2F1[13/8, 47/8, 3, z] == (1/(2919735 Pi (-1 + z)^5 z^2)) (128 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (16 (-1 + z) (322 - 805 z + 1872 z^2 - 1443 z^3 + 390 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 8 (-1 + z) (322 - 805 z + 1872 z^2 - 1443 z^3 + 390 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (-161 - 4186 z + 5343 z^2 - 2964 z^3 + 624 z^4) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (161 - 8050 z + 11401 z^2 - 6864 z^3 + 1560 z^4) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

 Standard Form

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 MathML Form

 2 F 1 ( 13 8 , 47 8 ; 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["13", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["47", "8"], 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] 1 2919735 π ( z - 1 ) 5 z 2 ( 128 2 3 / 4 1 - z + 1 4 ( 16 ( z - 1 ) ( 390 z 4 - 1443 z 3 + 1872 z 2 - 805 z + 322 ) E ( 1 2 - 1 2 1 - z + 1 ) - 8 ( z - 1 ) ( 390 z 4 - 1443 z 3 + 1872 z 2 - 805 z + 322 ) K ( 1 2 - 1 2 1 - z + 1 ) + 5 2 1 - z + 1 ( z - 1 ) ( 624 z 4 - 2964 z 3 + 5343 z 2 - 4186 z - 161 ) K ( 1 2 - 1 2 1 - z + 1 ) + 3 2 1 - z + 1 1 - z ( 1560 z 4 - 6864 z 3 + 11401 z 2 - 8050 z + 161 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ 13 8 47 8 3 z 1 2919735 z -1 5 z 2 -1 128 2 3 4 1 -1 z 1 2 1 1 4 16 z -1 390 z 4 -1 1443 z 3 1872 z 2 -1 805 z 322 EllipticE 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 -1 8 z -1 390 z 4 -1 1443 z 3 1872 z 2 -1 805 z 322 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 5 2 1 2 1 -1 z 1 2 1 1 2 z -1 624 z 4 -1 2964 z 3 5343 z 2 -1 4186 z -161 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 3 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 2 1560 z 4 -1 6864 z 3 11401 z 2 -1 8050 z 161 EllipticK 1 2 -1 1 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