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.ak3s.01

 Input Form

 Hypergeometric2F1[5/4, 21/4, 11/2, z] == (1/(43095 Pi^(3/2) z^(9/2))) (224 (-((2 (-1680 + 300 z + 203 z^2 + 208 z^3 + 384 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)) + (2 (-1680 + 300 z + 203 z^2 + 208 z^3 + 384 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z) + (1/(-1 + Sqrt[z])) ((-1680 + 840 Sqrt[z] - 540 z + 620 z^(3/2) - 417 z^2 + 496 z^(5/2) - 288 z^3 + 384 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])]) - (1/(1 + Sqrt[z])) ((1680 + 840 Sqrt[z] + 540 z + 620 z^(3/2) + 417 z^2 + 496 z^(5/2) + 288 z^3 + 384 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "4"], ",", FractionBox["21", "4"], ",", FractionBox["11", "2"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["43095", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]], RowBox[List["(", RowBox[List["224", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1680"]], "+", RowBox[List["300", " ", "z"]], "+", RowBox[List["203", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["208", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["384", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", "z"]]]]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1680"]], "+", RowBox[List["300", " ", "z"]], "+", RowBox[List["203", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["208", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["384", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", "z"]]], "+", RowBox[List[FractionBox["1", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1680"]], "+", RowBox[List["840", " ", SqrtBox["z"]]], "-", RowBox[List["540", " ", "z"]], "+", RowBox[List["620", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["417", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["496", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["288", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["384", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List["1", "+", SqrtBox["z"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1680", "+", RowBox[List["840", " ", SqrtBox["z"]]], "+", RowBox[List["540", " ", "z"]], "+", RowBox[List["620", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["417", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["496", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["288", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["384", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", 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 ( 5 4 , 21 4 ; 11 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["21", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["11", "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 43095 π 3 / 2 z 9 / 2 ( 224 ( - 2 ( 384 z 4 + 208 z 3 + 203 z 2 + 300 z - 1680 ) E ( 1 2 ( 1 - z ) ) z - 1 + 2 ( 384 z 4 + 208 z 3 + 203 z 2 + 300 z - 1680 ) E ( 1 2 ( z + 1 ) ) z - 1 + ( 384 z 7 / 2 - 288 z 3 + 496 z 5 / 2 - 417 z 2 + 620 z 3 / 2 - 540 z + 840 z - 1680 ) K ( 1 2 ( 1 - z ) ) z - 1 - ( 384 z 7 / 2 + 288 z 3 + 496 z 5 / 2 + 417 z 2 + 620 z 3 / 2 + 540 z + 840 z + 1680 ) K ( 1 2 ( z + 1 ) ) z + 1 ) Γ ( 3 4 ) 2 ) HypergeometricPFQ 5 4 21 4 11 2 z 1 43095 3 2 z 9 2 -1 224 -1 2 384 z 4 208 z 3 203 z 2 300 z -1680 EllipticE 1 2 1 -1 z 1 2 z -1 -1 2 384 z 4 208 z 3 203 z 2 300 z -1680 EllipticE 1 2 z 1 2 1 z -1 -1 384 z 7 2 -1 288 z 3 496 z 5 2 -1 417 z 2 620 z 3 2 -1 540 z 840 z 1 2 -1680 EllipticK 1 2 1 -1 z 1 2 z 1 2 -1 -1 -1 384 z 7 2 288 z 3 496 z 5 2 417 z 2 620 z 3 2 540 z 840 z 1 2 1680 EllipticK 1 2 z 1 2 1 z 1 2 1 -1 Gamma 3 4 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "4"], ",", FractionBox["21", "4"], ",", FractionBox["11", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["224", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1680"]], "+", RowBox[List["300", " ", "z"]], "+", RowBox[List["203", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["208", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["384", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", "z"]]]]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1680"]], "+", RowBox[List["300", " ", "z"]], "+", RowBox[List["203", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["208", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["384", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", "z"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1680"]], "+", RowBox[List["840", " ", SqrtBox["z"]]], "-", RowBox[List["540", " ", "z"]], "+", RowBox[List["620", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["417", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["496", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["288", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["384", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1680", "+", RowBox[List["840", " ", SqrtBox["z"]]], "+", RowBox[List["540", " ", "z"]], "+", RowBox[List["620", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["417", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["496", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["288", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["384", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List["1", "+", SqrtBox["z"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], RowBox[List["43095", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]]]]]]]]]

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

 2007-05-02