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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.ai5w.01

 Input Form

 Hypergeometric2F1[1/4, 9/4, -(7/2), z] == (1/(560 Pi^(3/2))) (((8 Sqrt[z] (70 - 405 z + 981 z^2 - 1308 z^3 - 1617 z^4 + 231 z^5) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^6 - (8 Sqrt[z] (70 - 405 z + 981 z^2 - 1308 z^3 - 1617 z^4 + 231 z^5) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^6 + (1/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^5)) ((560 - 840 Sqrt[z] - 2820 z + 4440 z^(3/2) + 5775 z^2 - 9699 z^(5/2) - 6318 z^3 + 11550 z^(7/2) + 5775 z^4 + 693 z^(9/2) - 924 z^5) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^6)) ((-560 - 840 Sqrt[z] + 2820 z + 4440 z^(3/2) - 5775 z^2 - 9699 z^(5/2) + 6318 z^3 + 11550 z^(7/2) - 5775 z^4 + 693 z^(9/2) + 924 z^5) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "4"], ",", FractionBox["9", "4"], ",", RowBox[List["-", FractionBox["7", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["560", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["70", "-", RowBox[List["405", " ", "z"]], "+", RowBox[List["981", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1308", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1617", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["231", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]], "-", FractionBox[RowBox[List["8", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["70", "-", RowBox[List["405", " ", "z"]], "+", RowBox[List["981", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1308", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1617", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["231", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]], "+", 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"]]], ")"]], "5"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["560", "-", RowBox[List["840", " ", SqrtBox["z"]]], "-", RowBox[List["2820", " ", "z"]], "+", RowBox[List["4440", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["5775", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["9699", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["6318", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["11550", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["5775", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["693", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["924", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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"]]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "6"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "560"]], "-", RowBox[List["840", " ", SqrtBox["z"]]], "+", RowBox[List["2820", " ", "z"]], "+", RowBox[List["4440", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["5775", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["9699", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["6318", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["11550", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["5775", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["693", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["924", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 1 4 , 9 4 ; - 7 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["1", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "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["7", "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] 1 560 π 3 / 2 ( ( 8 z ( 231 z 5 - 1617 z 4 - 1308 z 3 + 981 z 2 - 405 z + 70 ) E ( 1 2 ( 1 - z ) ) ( z - 1 ) 6 - 8 z ( 231 z 5 - 1617 z 4 - 1308 z 3 + 981 z 2 - 405 z + 70 ) E ( 1 2 ( z + 1 ) ) ( z - 1 ) 6 + 1 ( z - 1 ) 6 ( z + 1 ) 5 ( ( - 924 z 5 + 693 z 9 / 2 + 5775 z 4 + 11550 z 7 / 2 - 6318 z 3 - 9699 z 5 / 2 + 5775 z 2 + 4440 z 3 / 2 - 2820 z - 840 z + 560 ) K ( 1 2 ( 1 - z ) ) ) + 1 ( z - 1 ) 5 ( z + 1 ) 6 ( ( 924 z 5 + 693 z 9 / 2 - 5775 z 4 + 11550 z 7 / 2 + 6318 z 3 - 9699 z 5 / 2 - 5775 z 2 + 4440 z 3 / 2 + 2820 z - 840 z - 560 ) K ( 1 2 ( z + 1 ) ) ) ) Γ ( 3 4 ) 2 ) HypergeometricPFQ 1 4 9 4 -1 7 2 z 1 560 3 2 -1 8 z 1 2 231 z 5 -1 1617 z 4 -1 1308 z 3 981 z 2 -1 405 z 70 EllipticE 1 2 1 -1 z 1 2 z -1 6 -1 -1 8 z 1 2 231 z 5 -1 1617 z 4 -1 1308 z 3 981 z 2 -1 405 z 70 EllipticE 1 2 z 1 2 1 z -1 6 -1 1 z 1 2 -1 6 z 1 2 1 5 -1 -924 z 5 693 z 9 2 5775 z 4 11550 z 7 2 -1 6318 z 3 -1 9699 z 5 2 5775 z 2 4440 z 3 2 -1 2820 z -1 840 z 1 2 560 EllipticK 1 2 1 -1 z 1 2 1 z 1 2 -1 5 z 1 2 1 6 -1 924 z 5 693 z 9 2 -1 5775 z 4 11550 z 7 2 6318 z 3 -1 9699 z 5 2 -1 5775 z 2 4440 z 3 2 2820 z -1 840 z 1 2 -560 EllipticK 1 2 z 1 2 1 Gamma 3 4 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "4"], ",", FractionBox["9", "4"], ",", RowBox[List["-", FractionBox["7", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["70", "-", RowBox[List["405", " ", "z"]], "+", RowBox[List["981", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1308", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1617", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["231", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]], "-", FractionBox[RowBox[List["8", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["70", "-", RowBox[List["405", " ", "z"]], "+", RowBox[List["981", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1308", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1617", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["231", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "6"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["560", "-", RowBox[List["840", " ", SqrtBox["z"]]], "-", RowBox[List["2820", " ", "z"]], "+", RowBox[List["4440", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["5775", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["9699", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["6318", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["11550", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["5775", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["693", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "-", RowBox[List["924", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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"]]], ")"]], "5"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "560"]], "-", RowBox[List["840", " ", SqrtBox["z"]]], "+", RowBox[List["2820", " ", "z"]], "+", RowBox[List["4440", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["5775", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["9699", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["6318", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["11550", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["5775", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["693", " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]], "+", RowBox[List["924", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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"]]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "6"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], RowBox[List["560", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]]]]]]

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

 2007-05-02