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.accq.01

 Input Form

 Hypergeometric2F1[-(13/4), -(1/2), 2, z] == (1/(9945 Pi Sqrt[1 + Sqrt[1 - z]] z)) (2 Sqrt[2] (2 (390 + 16339 z + 6360 z^2 - 1312 z^3 + 168 z^4) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (390 + 16339 z + 6360 z^2 - 1312 z^3 + 168 z^4) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-390 - 6589 z - 392 z^2 + 56 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (390 + 16339 z + 6360 z^2 - 1312 z^3 + 168 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (390 + 16339 z + 6360 z^2 - 1312 z^3 + 168 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (390 + 16339 z + 6360 z^2 - 1312 z^3 + 168 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["13", "4"]]], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "2", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["9945", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", "z"]]], RowBox[List["(", RowBox[List["2", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["390", "+", RowBox[List["16339", " ", "z"]], "+", RowBox[List["6360", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["168", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["390", "+", RowBox[List["16339", " ", "z"]], "+", RowBox[List["6360", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["168", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "390"]], "-", RowBox[List["6589", " ", "z"]], "-", RowBox[List["392", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["56", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["390", "+", RowBox[List["16339", " ", "z"]], "+", RowBox[List["6360", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["168", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["390", "+", RowBox[List["16339", " ", "z"]], "+", RowBox[List["6360", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["168", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["390", "+", RowBox[List["16339", " ", "z"]], "+", RowBox[List["6360", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["168", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( - 13 4 , - 1 2 ; 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["13", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", 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[TagBox[TagBox["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 9945 π 1 - z + 1 z ( 2 2 ( 2 1 - z ( 168 z 4 - 1312 z 3 + 6360 z 2 + 16339 z + 390 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 2 ( 168 z 4 - 1312 z 3 + 6360 z 2 + 16339 z + 390 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 1 - z ) 3 / 4 ( 56 z 3 - 392 z 2 - 6589 z - 390 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - 1 - z ( 168 z 4 - 1312 z 3 + 6360 z 2 + 16339 z + 390 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - 1 - z 4 ( 168 z 4 - 1312 z 3 + 6360 z 2 + 16339 z + 390 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - ( 168 z 4 - 1312 z 3 + 6360 z 2 + 16339 z + 390 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ -1 13 4 -1 1 2 2 z 1 9945 1 -1 z 1 2 1 1 2 z -1 2 2 1 2 2 1 -1 z 1 2 168 z 4 -1 1312 z 3 6360 z 2 16339 z 390 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 2 168 z 4 -1 1312 z 3 6360 z 2 16339 z 390 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 4 56 z 3 -1 392 z 2 -1 6589 z -390 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 1 -1 z 1 2 168 z 4 -1 1312 z 3 6360 z 2 16339 z 390 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 1 -1 z 1 4 168 z 4 -1 1312 z 3 6360 z 2 16339 z 390 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 168 z 4 -1 1312 z 3 6360 z 2 16339 z 390 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["13", "4"]]], ",", RowBox[List["-", FractionBox["1", "2"]]], ",", "2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List["390", "+", RowBox[List["16339", " ", "z"]], "+", RowBox[List["6360", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["168", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["390", "+", RowBox[List["16339", " ", "z"]], "+", RowBox[List["6360", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["168", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "390"]], "-", RowBox[List["6589", " ", "z"]], "-", RowBox[List["392", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["56", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["390", "+", RowBox[List["16339", " ", "z"]], "+", RowBox[List["6360", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["168", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["390", "+", RowBox[List["16339", " ", "z"]], "+", RowBox[List["6360", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["168", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["390", "+", RowBox[List["16339", " ", "z"]], "+", RowBox[List["6360", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["1312", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["168", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["9945", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", "z"]]]]]]]

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

 2007-05-02