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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c6ro.01

 Input Form

 Hypergeometric2F1[17/8, 45/8, 5, z] == (65536 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-1024 + 1696 z - 99 z^2 - 129 z^3 + 144 z^4) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-1024 + 1696 z - 99 z^2 - 129 z^3 + 144 z^4) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-1024 + 1696 z - 99 z^2 - 129 z^3 + 144 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-1 + z) (512 - 528 z - 213 z^2 - 108 z^3 + 288 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (30757545 Pi (1 + Sqrt[1 - z])^(1/4) (-1 + z)^3 z^4)

 Standard Form

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 MathML Form

 2 F 1 ( 17 8 , 45 8 ; 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["17", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["45", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["5", 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] ( 65536 2 4 ( - 2 2 1 - z + 1 1 - z 4 ( 144 z 4 - 129 z 3 - 99 z 2 + 1696 z - 1024 ) E ( 1 2 - 1 - z 4 2 1 - z + 1 ) + 1 - z ( 144 z 4 - 129 z 3 - 99 z 2 + 1696 z - 1024 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) + 2 1 - z + 1 1 - z 4 ( 144 z 4 - 129 z 3 - 99 z 2 + 1696 z - 1024 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) + 2 ( z - 1 ) ( 288 z 4 - 108 z 3 - 213 z 2 - 528 z + 512 ) K ( 1 2 - 1 - z 4 2 1 - z + 1 ) ) ) / ( 30757545 π 1 - z + 1 4 ( z - 1 ) 3 z 4 ) HypergeometricPFQ 17 8 45 8 5 z 65536 2 1 4 -2 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 4 144 z 4 -1 129 z 3 -1 99 z 2 1696 z -1024 EllipticE 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 1 -1 z 1 2 144 z 4 -1 129 z 3 -1 99 z 2 1696 z -1024 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 2 1 2 1 -1 z 1 2 1 1 2 1 -1 z 1 4 144 z 4 -1 129 z 3 -1 99 z 2 1696 z -1024 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 2 z -1 288 z 4 -1 108 z 3 -1 213 z 2 -1 528 z 512 EllipticK 1 2 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 2 1 1 2 -1 30757545 1 -1 z 1 2 1 1 4 z -1 3 z 4 -1 [/itex]

 Rule Form

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

 2007-05-02