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.c1h2.01

 Input Form

 Hypergeometric2F1[7/8, 45/8, 6, z] == (1/(4108329225 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (32768 + 22656 z + 19459 z^2 + 18172 z^3 + 18480 z^4) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 20 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1024 + 876 z + 803 z^2 + 770 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1/Sqrt[1 - z]) (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (4096 + 1712 z + 1133 z^2 + 924 z^3 + 6160 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) + 2 (32768 + 22656 z + 19459 z^2 + 18172 z^3 + 18480 z^4) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["7", "8"], ",", FractionBox["45", "8"], ",", "6", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["4108329225", " ", "\[Pi]", " ", SuperscriptBox["z", "5"]]]], RowBox[List["(", RowBox[List["262144", " ", SuperscriptBox["2", RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List["32768", "+", RowBox[List["22656", " ", "z"]], "+", RowBox[List["19459", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["18172", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18480", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List["20", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List["1024", "+", RowBox[List["876", " ", "z"]], "+", RowBox[List["803", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["770", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "-", "z"]]]], RowBox[List["3", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List["4096", "+", RowBox[List["1712", " ", "z"]], "+", RowBox[List["1133", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["924", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["6160", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["32768", "+", RowBox[List["22656", " ", "z"]], "+", RowBox[List["19459", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["18172", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18480", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 7 8 , 45 8 ; 6 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["45", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["6", 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 4108329225 π z 5 ( 262144 2 3 / 4 1 - z + 1 4 ( - 4 ( 18480 z 4 + 18172 z 3 + 19459 z 2 + 22656 z + 32768 ) E ( 1 2 - 1 2 1 - z + 1 ) + 20 2 1 - z + 1 ( 770 z 3 + 803 z 2 + 876 z + 1024 ) K ( 1 2 - 1 2 1 - z + 1 ) + 3 2 1 - z + 1 ( 6160 z 4 + 924 z 3 + 1133 z 2 + 1712 z + 4096 ) K ( 1 2 - 1 2 1 - z + 1 ) 1 - z + 2 ( 18480 z 4 + 18172 z 3 + 19459 z 2 + 22656 z + 32768 ) K ( 1 2 - 1 2 1 - z + 1 ) ) ) HypergeometricPFQ 7 8 45 8 6 z 1 4108329225 z 5 -1 262144 2 3 4 1 -1 z 1 2 1 1 4 -4 18480 z 4 18172 z 3 19459 z 2 22656 z 32768 EllipticE 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 20 2 1 2 1 -1 z 1 2 1 1 2 770 z 3 803 z 2 876 z 1024 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 3 2 1 2 1 -1 z 1 2 1 1 2 6160 z 4 924 z 3 1133 z 2 1712 z 4096 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 1 -1 z 1 2 -1 2 18480 z 4 18172 z 3 19459 z 2 22656 z 32768 EllipticK 1 2 -1 1 2 1 2 1 -1 z 1 2 1 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["7", "8"], ",", FractionBox["45", "8"], ",", "6", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["262144", " ", SuperscriptBox["2", RowBox[List["3", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", RowBox[List["(", RowBox[List["32768", "+", RowBox[List["22656", " ", "z"]], "+", RowBox[List["19459", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["18172", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18480", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", RowBox[List["20", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List["1024", "+", RowBox[List["876", " ", "z"]], "+", RowBox[List["803", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["770", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], "+", FractionBox[RowBox[List["3", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", RowBox[List["(", RowBox[List["4096", "+", RowBox[List["1712", " ", "z"]], "+", RowBox[List["1133", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["924", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["6160", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]], SqrtBox[RowBox[List["1", "-", "z"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["32768", "+", RowBox[List["22656", " ", "z"]], "+", RowBox[List["19459", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["18172", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["18480", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["4108329225", " ", "\[Pi]", " ", SuperscriptBox["z", "5"]]]]]]]]

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

 2007-05-02