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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ak3i.01

 Input Form

 Hypergeometric2F1[5/4, 21/4, 3, -z] == (1/(9945 Pi z^2 Sqrt[1 + Sqrt[1 + z]])) (64 Sqrt[2] ((4 (15 + 15 z + 98 z^2 + 100 z^3 + 32 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(7/2) + (4 (15 + 15 z + 98 z^2 + 100 z^3 + 32 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^3 - ((60 + 45 z + 77 z^2 + 32 z^3) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])])/(1 + z)^3 - (4 (15 + 15 z + 98 z^2 + 100 z^3 + 32 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(7/2)))

 Standard Form

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 MathML Form

 2 F 1 ( 5 4 , 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["5", "4"], 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[RowBox[List["-", "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 9945 π z 2 z + 1 + 1 ( 64 2 ( 4 ( 32 z 4 + 100 z 3 + 98 z 2 + 15 z + 15 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 3 + 4 ( 32 z 4 + 100 z 3 + 98 z 2 + 15 z + 15 ) E ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 7 / 2 - ( 32 z 3 + 77 z 2 + 45 z + 60 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 3 - 4 ( 32 z 4 + 100 z 3 + 98 z 2 + 15 z + 15 ) K ( z + 1 - 1 z + 1 + 1 ) ( z + 1 ) 7 / 2 ) ) HypergeometricPFQ 5 4 21 4 3 -1 z 1 9945 z 2 z 1 1 2 1 1 2 -1 64 2 1 2 4 32 z 4 100 z 3 98 z 2 15 z 15 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 3 -1 4 32 z 4 100 z 3 98 z 2 15 z 15 EllipticE z 1 1 2 -1 z 1 1 2 1 -1 z 1 7 2 -1 -1 32 z 3 77 z 2 45 z 60 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 3 -1 -1 4 32 z 4 100 z 3 98 z 2 15 z 15 EllipticK z 1 1 2 -1 z 1 1 2 1 -1 z 1 7 2 -1 [/itex]

 Rule Form

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

 2007-05-02