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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.amo8.01

 Input Form

 Hypergeometric2F1[15/4, 15/4, 1/2, z] == (1/(71148 Pi^(3/2))) ((-((2 (17787 + 349455 z + 527729 z^2 + 88069 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^7) - (2 (17787 + 349455 z + 527729 z^2 + 88069 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^7 + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^6)) ((17787 + 48144 Sqrt[z] + 301311 z + 154592 z^(3/2) + 373137 z^2 + 43024 z^(5/2) + 45045 z^3) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^7)) ((-17787 + 48144 Sqrt[z] - 301311 z + 154592 z^(3/2) - 373137 z^2 + 43024 z^(5/2) - 45045 z^3) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["15", "4"], ",", FractionBox["15", "4"], ",", FractionBox["1", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["71148", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["17787", "+", RowBox[List["349455", " ", "z"]], "+", RowBox[List["527729", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["88069", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"]]]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["17787", "+", RowBox[List["349455", " ", "z"]], "+", RowBox[List["527729", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["88069", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"]], "+", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "6"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["17787", "+", RowBox[List["48144", " ", SqrtBox["z"]]], "+", RowBox[List["301311", " ", "z"]], "+", RowBox[List["154592", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["373137", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["43024", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["45045", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "7"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "17787"]], "+", RowBox[List["48144", " ", SqrtBox["z"]]], "-", RowBox[List["301311", " ", "z"]], "+", RowBox[List["154592", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["373137", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["43024", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["45045", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 15 4 , 15 4 ; 1 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["15", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["15", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["1", "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 71148 π 3 / 2 ( ( - 2 ( 88069 z 3 + 527729 z 2 + 349455 z + 17787 ) E ( 1 2 ( 1 - z ) ) ( z - 1 ) 7 - 2 ( 88069 z 3 + 527729 z 2 + 349455 z + 17787 ) E ( 1 2 ( z + 1 ) ) ( z - 1 ) 7 + 1 ( z - 1 ) 7 ( z + 1 ) 6 ( 45045 z 3 + 43024 z 5 / 2 + 373137 z 2 + 154592 z 3 / 2 + 301311 z + 48144 z + 17787 ) K ( 1 2 ( 1 - z ) ) + 1 ( z - 1 ) 6 ( z + 1 ) 7 ( - 45045 z 3 + 43024 z 5 / 2 - 373137 z 2 + 154592 z 3 / 2 - 301311 z + 48144 z - 17787 ) K ( 1 2 ( z + 1 ) ) ) Γ ( 1 4 ) 2 ) HypergeometricPFQ 15 4 15 4 1 2 z 1 71148 3 2 -1 -1 2 88069 z 3 527729 z 2 349455 z 17787 EllipticE 1 2 1 -1 z 1 2 z -1 7 -1 -1 2 88069 z 3 527729 z 2 349455 z 17787 EllipticE 1 2 z 1 2 1 z -1 7 -1 1 z 1 2 -1 7 z 1 2 1 6 -1 45045 z 3 43024 z 5 2 373137 z 2 154592 z 3 2 301311 z 48144 z 1 2 17787 EllipticK 1 2 1 -1 z 1 2 1 z 1 2 -1 6 z 1 2 1 7 -1 -45045 z 3 43024 z 5 2 -1 373137 z 2 154592 z 3 2 -1 301311 z 48144 z 1 2 -17787 EllipticK 1 2 z 1 2 1 Gamma 1 4 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["15", "4"], ",", FractionBox["15", "4"], ",", FractionBox["1", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["17787", "+", RowBox[List["349455", " ", "z"]], "+", RowBox[List["527729", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["88069", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"]]]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["17787", "+", RowBox[List["349455", " ", "z"]], "+", RowBox[List["527729", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["88069", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "7"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["17787", "+", RowBox[List["48144", " ", SqrtBox["z"]]], "+", RowBox[List["301311", " ", "z"]], "+", RowBox[List["154592", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["373137", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["43024", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["45045", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "6"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "17787"]], "+", RowBox[List["48144", " ", SqrtBox["z"]]], "-", RowBox[List["301311", " ", "z"]], "+", RowBox[List["154592", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["373137", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["43024", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["45045", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "7"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], RowBox[List["71148", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]]]]]]

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

 2007-05-02