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.ajza.01

 Input Form

 Hypergeometric2F1[5/4, 17/4, 3/2, z] == (1/(585 Pi^(3/2) Sqrt[z])) (2 (-((2 (231 + 258 z - 137 z^2 + 32 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/ (-1 + z)^4) + (2 (231 + 258 z - 137 z^2 + 32 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^4 + ((231 + 177 Sqrt[z] + 81 z - 113 z^(3/2) - 24 z^2 + 32 z^(5/2)) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^3) - ((-231 + 177 Sqrt[z] - 81 z - 113 z^(3/2) + 24 z^2 + 32 z^(5/2)) EllipticK[(1/2) (1 + Sqrt[z])])/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^4)) Gamma[3/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "4"], ",", FractionBox["17", "4"], ",", FractionBox["3", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["585", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SqrtBox["z"]]]], RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["231", "+", RowBox[List["258", " ", "z"]], "-", RowBox[List["137", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", 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"]], ")"]], "4"]]]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["231", "+", RowBox[List["258", " ", "z"]], "-", RowBox[List["137", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", 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"]], ")"]], "4"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["231", "+", RowBox[List["177", " ", SqrtBox["z"]]], "+", RowBox[List["81", " ", "z"]], "-", RowBox[List["113", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", 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"]]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "3"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "231"]], "+", RowBox[List["177", " ", SqrtBox["z"]]], "-", RowBox[List["81", " ", "z"]], "-", RowBox[List["113", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", 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"]]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "4"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 5 4 , 17 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["17", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[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] 1 585 π 3 / 2 z ( 2 ( - 2 ( 32 z 3 - 137 z 2 + 258 z + 231 ) E ( 1 2 ( 1 - z ) ) ( z - 1 ) 4 + 2 ( 32 z 3 - 137 z 2 + 258 z + 231 ) E ( 1 2 ( z + 1 ) ) ( z - 1 ) 4 + ( 32 z 5 / 2 - 24 z 2 - 113 z 3 / 2 + 81 z + 177 z + 231 ) K ( 1 2 ( 1 - z ) ) ( z - 1 ) 4 ( z + 1 ) 3 - ( 32 z 5 / 2 + 24 z 2 - 113 z 3 / 2 - 81 z + 177 z - 231 ) K ( 1 2 ( z + 1 ) ) ( z - 1 ) 3 ( z + 1 ) 4 ) Γ ( 3 4 ) 2 ) HypergeometricPFQ 5 4 17 4 3 2 z 1 585 3 2 z 1 2 -1 2 -1 2 32 z 3 -1 137 z 2 258 z 231 EllipticE 1 2 1 -1 z 1 2 z -1 4 -1 2 32 z 3 -1 137 z 2 258 z 231 EllipticE 1 2 z 1 2 1 z -1 4 -1 32 z 5 2 -1 24 z 2 -1 113 z 3 2 81 z 177 z 1 2 231 EllipticK 1 2 1 -1 z 1 2 z 1 2 -1 4 z 1 2 1 3 -1 -1 32 z 5 2 24 z 2 -1 113 z 3 2 -1 81 z 177 z 1 2 -231 EllipticK 1 2 z 1 2 1 z 1 2 -1 3 z 1 2 1 4 -1 Gamma 3 4 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "4"], ",", FractionBox["17", "4"], ",", FractionBox["3", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["231", "+", RowBox[List["258", " ", "z"]], "-", RowBox[List["137", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", 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"]], ")"]], "4"]]]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["231", "+", RowBox[List["258", " ", "z"]], "-", RowBox[List["137", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", 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"]], ")"]], "4"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["231", "+", RowBox[List["177", " ", SqrtBox["z"]]], "+", RowBox[List["81", " ", "z"]], "-", RowBox[List["113", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", 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"]]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "3"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "231"]], "+", RowBox[List["177", " ", SqrtBox["z"]]], "-", RowBox[List["81", " ", "z"]], "-", RowBox[List["113", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["24", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]], ")"]], " ", 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"]]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "4"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], RowBox[List["585", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SqrtBox["z"]]]]]]]]

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

 2007-05-02