html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.amo6.01

 Input Form

 Hypergeometric2F1[15/4, 15/4, -(1/2), z] == (1/(142296 Pi^(3/2))) ((-((1/(-1 + z)^8) (4 (-17787 + 640332 z + 6179326 z^2 + 6189580 z^3 + 771109 z^4) EllipticE[(1/2) (1 - Sqrt[z])])) - (1/(-1 + z)^8) (4 (-17787 + 640332 z + 6179326 z^2 + 6189580 z^3 + 771109 z^4) EllipticE[(1/2) (1 + Sqrt[z])]) + (1/((-1 + Sqrt[z])^8 (1 + Sqrt[z])^7)) ((-35574 + 17787 Sqrt[z] + 1262877 z + 2123279 z^(3/2) + 10235373 z^2 + 3963761 z^(5/2) + 8415399 z^3 + 776453 z^(7/2) + 765765 z^4) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^7 (1 + Sqrt[z])^8)) ((35574 + 17787 Sqrt[z] - 1262877 z + 2123279 z^(3/2) - 10235373 z^2 + 3963761 z^(5/2) - 8415399 z^3 + 776453 z^(7/2) - 765765 z^4) 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"], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["142296", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "8"]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "17787"]], "+", RowBox[List["640332", " ", "z"]], "+", RowBox[List["6179326", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["6189580", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["771109", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]]]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "8"]], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "17787"]], "+", RowBox[List["640332", " ", "z"]], "+", RowBox[List["6179326", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["6189580", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["771109", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", 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"]]], ")"]], "8"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "7"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "35574"]], "+", RowBox[List["17787", " ", SqrtBox["z"]]], "+", RowBox[List["1262877", " ", "z"]], "+", RowBox[List["2123279", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["10235373", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3963761", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["8415399", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["776453", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["765765", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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"]]], ")"]], "7"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "8"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["35574", "+", RowBox[List["17787", " ", SqrtBox["z"]]], "-", RowBox[List["1262877", " ", "z"]], "+", RowBox[List["2123279", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["10235373", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3963761", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["8415399", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["776453", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["765765", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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[RowBox[List["-", 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 142296 π 3 / 2 ( ( - 4 ( 771109 z 4 + 6189580 z 3 + 6179326 z 2 + 640332 z - 17787 ) E ( 1 2 ( 1 - z ) ) ( z - 1 ) 8 - 4 ( 771109 z 4 + 6189580 z 3 + 6179326 z 2 + 640332 z - 17787 ) E ( 1 2 ( z + 1 ) ) ( z - 1 ) 8 + 1 ( z - 1 ) 8 ( z + 1 ) 7 ( ( 765765 z 4 + 776453 z 7 / 2 + 8415399 z 3 + 3963761 z 5 / 2 + 10235373 z 2 + 2123279 z 3 / 2 + 1262877 z + 17787 z - 35574 ) K ( 1 2 ( 1 - z ) ) ) + 1 ( z - 1 ) 7 ( z + 1 ) 8 ( ( - 765765 z 4 + 776453 z 7 / 2 - 8415399 z 3 + 3963761 z 5 / 2 - 10235373 z 2 + 2123279 z 3 / 2 - 1262877 z + 17787 z + 35574 ) K ( 1 2 ( z + 1 ) ) ) ) Γ ( 1 4 ) 2 ) HypergeometricPFQ 15 4 15 4 -1 1 2 z 1 142296 3 2 -1 -1 4 771109 z 4 6189580 z 3 6179326 z 2 640332 z -17787 EllipticE 1 2 1 -1 z 1 2 z -1 8 -1 -1 4 771109 z 4 6189580 z 3 6179326 z 2 640332 z -17787 EllipticE 1 2 z 1 2 1 z -1 8 -1 1 z 1 2 -1 8 z 1 2 1 7 -1 765765 z 4 776453 z 7 2 8415399 z 3 3963761 z 5 2 10235373 z 2 2123279 z 3 2 1262877 z 17787 z 1 2 -35574 EllipticK 1 2 1 -1 z 1 2 1 z 1 2 -1 7 z 1 2 1 8 -1 -765765 z 4 776453 z 7 2 -1 8415399 z 3 3963761 z 5 2 -1 10235373 z 2 2123279 z 3 2 -1 1262877 z 17787 z 1 2 35574 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"], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "17787"]], "+", RowBox[List["640332", " ", "z"]], "+", RowBox[List["6179326", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["6189580", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["771109", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "8"]]]], "-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "17787"]], "+", RowBox[List["640332", " ", "z"]], "+", RowBox[List["6179326", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["6189580", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["771109", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "8"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "35574"]], "+", RowBox[List["17787", " ", SqrtBox["z"]]], "+", RowBox[List["1262877", " ", "z"]], "+", RowBox[List["2123279", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["10235373", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3963761", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["8415399", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["776453", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["765765", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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"]]], ")"]], "8"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "7"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["35574", "+", RowBox[List["17787", " ", SqrtBox["z"]]], "-", RowBox[List["1262877", " ", "z"]], "+", RowBox[List["2123279", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["10235373", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["3963761", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["8415399", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["776453", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["765765", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", 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"]]], ")"]], "8"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], RowBox[List["142296", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]]]]]]

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

 2007-05-02