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.aisp.01

 Input Form

 Hypergeometric2F1[3/4, 3/4, -(7/2), z] == (1/(6720 Pi^(3/2))) ((-((2 (1680 - 8460 z + 17341 z^2 - 18806 z^3 + 14389 z^4) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^5) - (2 (1680 - 8460 z + 17341 z^2 - 18806 z^3 + 14389 z^4) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^5 + (1/((-1 + Sqrt[z])^5 (1 + Sqrt[z])^4)) ((1680 - 840 Sqrt[z] - 7620 z + 3460 z^(3/2) + 13881 z^2 - 5528 z^(5/2) - 13278 z^3 + 4444 z^(7/2) + 9945 z^4) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^4 (1 + Sqrt[z])^5)) ((-1680 - 840 Sqrt[z] + 7620 z + 3460 z^(3/2) - 13881 z^2 - 5528 z^(5/2) + 13278 z^3 + 4444 z^(7/2) - 9945 z^4) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["3", "4"], ",", FractionBox["3", "4"], ",", RowBox[List["-", FractionBox["7", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["6720", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1680", "-", RowBox[List["8460", " ", "z"]], "+", RowBox[List["17341", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["18806", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["14389", " ", 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"]], ")"]], "5"]]]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1680", "-", RowBox[List["8460", " ", "z"]], "+", RowBox[List["17341", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["18806", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["14389", " ", 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"]], ")"]], "5"]], "+", 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"]]], ")"]], "4"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1680", "-", RowBox[List["840", " ", SqrtBox["z"]]], "-", RowBox[List["7620", " ", "z"]], "+", RowBox[List["3460", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["13881", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["5528", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["13278", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["4444", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["9945", " ", 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"]]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "5"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1680"]], "-", RowBox[List["840", " ", SqrtBox["z"]]], "+", RowBox[List["7620", " ", "z"]], "+", RowBox[List["3460", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["13881", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["5528", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["13278", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["4444", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["9945", " ", 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 ( 3 4 , 3 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["3", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "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 6720 π 3 / 2 ( ( - 2 ( 14389 z 4 - 18806 z 3 + 17341 z 2 - 8460 z + 1680 ) E ( 1 2 ( 1 - z ) ) ( z - 1 ) 5 - 2 ( 14389 z 4 - 18806 z 3 + 17341 z 2 - 8460 z + 1680 ) E ( 1 2 ( z + 1 ) ) ( z - 1 ) 5 + 1 ( z - 1 ) 5 ( z + 1 ) 4 ( ( 9945 z 4 + 4444 z 7 / 2 - 13278 z 3 - 5528 z 5 / 2 + 13881 z 2 + 3460 z 3 / 2 - 7620 z - 840 z + 1680 ) K ( 1 2 ( 1 - z ) ) ) + 1 ( z - 1 ) 4 ( z + 1 ) 5 ( ( - 9945 z 4 + 4444 z 7 / 2 + 13278 z 3 - 5528 z 5 / 2 - 13881 z 2 + 3460 z 3 / 2 + 7620 z - 840 z - 1680 ) K ( 1 2 ( z + 1 ) ) ) ) Γ ( 1 4 ) 2 ) HypergeometricPFQ 3 4 3 4 -1 7 2 z 1 6720 3 2 -1 -1 2 14389 z 4 -1 18806 z 3 17341 z 2 -1 8460 z 1680 EllipticE 1 2 1 -1 z 1 2 z -1 5 -1 -1 2 14389 z 4 -1 18806 z 3 17341 z 2 -1 8460 z 1680 EllipticE 1 2 z 1 2 1 z -1 5 -1 1 z 1 2 -1 5 z 1 2 1 4 -1 9945 z 4 4444 z 7 2 -1 13278 z 3 -1 5528 z 5 2 13881 z 2 3460 z 3 2 -1 7620 z -1 840 z 1 2 1680 EllipticK 1 2 1 -1 z 1 2 1 z 1 2 -1 4 z 1 2 1 5 -1 -9945 z 4 4444 z 7 2 13278 z 3 -1 5528 z 5 2 -1 13881 z 2 3460 z 3 2 7620 z -1 840 z 1 2 -1680 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["3", "4"], ",", FractionBox["3", "4"], ",", RowBox[List["-", FractionBox["7", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1680", "-", RowBox[List["8460", " ", "z"]], "+", RowBox[List["17341", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["18806", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["14389", " ", 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"]], ")"]], "5"]]]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["1680", "-", RowBox[List["8460", " ", "z"]], "+", RowBox[List["17341", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["18806", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["14389", " ", 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"]], ")"]], "5"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1680", "-", RowBox[List["840", " ", SqrtBox["z"]]], "-", RowBox[List["7620", " ", "z"]], "+", RowBox[List["3460", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["13881", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["5528", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["13278", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["4444", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["9945", " ", 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"]]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "4"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1680"]], "-", RowBox[List["840", " ", SqrtBox["z"]]], "+", RowBox[List["7620", " ", "z"]], "+", RowBox[List["3460", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["13881", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["5528", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["13278", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["4444", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["9945", " ", 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"]]], ")"]], "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "5"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], RowBox[List["6720", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]]]]]]

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

 2007-05-02