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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ajv2.01

 Input Form

 Hypergeometric2F1[5/4, 13/4, -(3/2), z] == (1/(180 Pi^(3/2))) (((4 Sqrt[z] (45 - 375 z - 18687 z^2 - 1617 z^3 + 154 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^6 - (4 Sqrt[z] (45 - 375 z - 18687 z^2 - 1617 z^3 + 154 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^6 + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^5)) ((180 - 270 Sqrt[z] - 1365 z + 2115 z^(3/2) + 8730 z^2 + 28644 z^(5/2) + 3003 z^3 + 231 z^(7/2) - 308 z^4) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^6)) ((-180 - 270 Sqrt[z] + 1365 z + 2115 z^(3/2) - 8730 z^2 + 28644 z^(5/2) - 3003 z^3 + 231 z^(7/2) + 308 z^4) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)

 Standard Form

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 MathML Form

 2 F 1 ( 5 4 , 13 4 ; - 3 2 ; 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["13", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["3", "2"]]], 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] 1 180 π 3 / 2 ( ( 4 z ( 154 z 4 - 1617 z 3 - 18687 z 2 - 375 z + 45 ) E ( 1 2 ( 1 - z ) ) ( z - 1 ) 6 - 4 z ( 154 z 4 - 1617 z 3 - 18687 z 2 - 375 z + 45 ) E ( 1 2 ( z + 1 ) ) ( z - 1 ) 6 + 1 ( z - 1 ) 6 ( z + 1 ) 5 ( - 308 z 4 + 231 z 7 / 2 + 3003 z 3 + 28644 z 5 / 2 + 8730 z 2 + 2115 z 3 / 2 - 1365 z - 270 z + 180 ) K ( 1 2 ( 1 - z ) ) + 1 ( z - 1 ) 5 ( z + 1 ) 6 ( 308 z 4 + 231 z 7 / 2 - 3003 z 3 + 28644 z 5 / 2 - 8730 z 2 + 2115 z 3 / 2 + 1365 z - 270 z - 180 ) K ( 1 2 ( z + 1 ) ) ) Γ ( 3 4 ) 2 ) HypergeometricPFQ 5 4 13 4 -1 3 2 z 1 180 3 2 -1 4 z 1 2 154 z 4 -1 1617 z 3 -1 18687 z 2 -1 375 z 45 EllipticE 1 2 1 -1 z 1 2 z -1 6 -1 -1 4 z 1 2 154 z 4 -1 1617 z 3 -1 18687 z 2 -1 375 z 45 EllipticE 1 2 z 1 2 1 z -1 6 -1 1 z 1 2 -1 6 z 1 2 1 5 -1 -308 z 4 231 z 7 2 3003 z 3 28644 z 5 2 8730 z 2 2115 z 3 2 -1 1365 z -1 270 z 1 2 180 EllipticK 1 2 1 -1 z 1 2 1 z 1 2 -1 5 z 1 2 1 6 -1 308 z 4 231 z 7 2 -1 3003 z 3 28644 z 5 2 -1 8730 z 2 2115 z 3 2 1365 z -1 270 z 1 2 -180 EllipticK 1 2 z 1 2 1 Gamma 3 4 2 [/itex]

 Rule Form

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

 2007-05-02