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/07.23.03.9083.01

 Input Form

 Hypergeometric2F1[-(23/4), -(17/4), 3, -z] == -((1/(466821830475 Pi z^2)) (64 (1 + z)^(1/4) ((8498776 + 410065942 z - 52644356340 z^2 + 330014247930 z^3 - 507502537440 z^4 + 221387298282 z^5 - 21914032836 z^6 + 7326150 z^7) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + (-4249388 (1 + Sqrt[1 + z]) + 3663075 z^7 (-1 + 2 Sqrt[1 + z]) - 1062347 z (193 + 190 Sqrt[1 + z]) + 6 z^6 (1826169403 + 107450200 Sqrt[1 + z]) + 30 z^2 (877405939 + 396162748 Sqrt[1 + z]) - 27 z^5 (4099764783 + 593336258 Sqrt[1 + z]) + 60 z^4 (4229187812 + 979906619 Sqrt[1 + z]) - 15 z^3 (11000474931 + 3613306042 Sqrt[1 + z])) EllipticK[1/2 - 1/(2 Sqrt[1 + z])])))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["23", "4"]]], ",", RowBox[List["-", FractionBox["17", "4"]]], ",", "3", ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["466821830475", " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List["64", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["8498776", "+", RowBox[List["410065942", " ", "z"]], "-", RowBox[List["52644356340", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["330014247930", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["507502537440", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["221387298282", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["21914032836", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["7326150", " ", SuperscriptBox["z", "7"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4249388"]], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]]]], "+", RowBox[List["3663075", " ", SuperscriptBox["z", "7"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]], "-", RowBox[List["1062347", " ", "z", " ", RowBox[List["(", RowBox[List["193", "+", RowBox[List["190", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]], "+", RowBox[List["6", " ", SuperscriptBox["z", "6"], " ", RowBox[List["(", RowBox[List["1826169403", "+", RowBox[List["107450200", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]], "+", RowBox[List["30", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["877405939", "+", RowBox[List["396162748", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]], "-", RowBox[List["27", " ", SuperscriptBox["z", "5"], " ", RowBox[List["(", RowBox[List["4099764783", "+", RowBox[List["593336258", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]], "+", RowBox[List["60", " ", SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List["4229187812", "+", RowBox[List["979906619", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]], "-", RowBox[List["15", " ", SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List["11000474931", "+", RowBox[List["3613306042", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]]]

 MathML Form

 2 F 1 ( - 23 4 , - 17 4 ; 3 ; - 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["23", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", 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["3", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "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 466821830475 π z 2 ( 64 z + 1 4 ( ( 7326150 z 7 - 21914032836 z 6 + 221387298282 z 5 - 507502537440 z 4 + 330014247930 z 3 - 52644356340 z 2 + 410065942 z + 8498776 ) E ( 1 2 - 1 2 z + 1 ) + ( 3663075 ( 2 z + 1 - 1 ) z 7 + 6 ( 107450200 z + 1 + 1826169403 ) z 6 - 27 ( 593336258 z + 1 + 4099764783 ) z 5 + 60 ( 979906619 z + 1 + 4229187812 ) z 4 - 15 ( 3613306042 z + 1 + 11000474931 ) z 3 + 30 ( 396162748 z + 1 + 877405939 ) z 2 - 1062347 ( 190 z + 1 + 193 ) z - 4249388 ( z + 1 + 1 ) ) K ( 1 2 - 1 2 z + 1 ) ) ) HypergeometricPFQ -1 23 4 -1 17 4 3 -1 z -1 1 466821830475 z 2 -1 64 z 1 1 4 7326150 z 7 -1 21914032836 z 6 221387298282 z 5 -1 507502537440 z 4 330014247930 z 3 -1 52644356340 z 2 410065942 z 8498776 EllipticE 1 2 -1 1 2 z 1 1 2 -1 3663075 2 z 1 1 2 -1 z 7 6 107450200 z 1 1 2 1826169403 z 6 -1 27 593336258 z 1 1 2 4099764783 z 5 60 979906619 z 1 1 2 4229187812 z 4 -1 15 3613306042 z 1 1 2 11000474931 z 3 30 396162748 z 1 1 2 877405939 z 2 -1 1062347 190 z 1 1 2 193 z -1 4249388 z 1 1 2 1 EllipticK 1 2 -1 1 2 z 1 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["23", "4"]]], ",", RowBox[List["-", FractionBox["17", "4"]]], ",", "3", ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["64", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["8498776", "+", RowBox[List["410065942", " ", "z"]], "-", RowBox[List["52644356340", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["330014247930", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["507502537440", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["221387298282", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["21914032836", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["7326150", " ", SuperscriptBox["z", "7"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "4249388"]], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], ")"]]]], "+", RowBox[List["3663075", " ", SuperscriptBox["z", "7"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]], "-", RowBox[List["1062347", " ", "z", " ", RowBox[List["(", RowBox[List["193", "+", RowBox[List["190", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]], "+", RowBox[List["6", " ", SuperscriptBox["z", "6"], " ", RowBox[List["(", RowBox[List["1826169403", "+", RowBox[List["107450200", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]], "+", RowBox[List["30", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["877405939", "+", RowBox[List["396162748", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]], "-", RowBox[List["27", " ", SuperscriptBox["z", "5"], " ", RowBox[List["(", RowBox[List["4099764783", "+", RowBox[List["593336258", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]], "+", RowBox[List["60", " ", SuperscriptBox["z", "4"], " ", RowBox[List["(", RowBox[List["4229187812", "+", RowBox[List["979906619", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]], "-", RowBox[List["15", " ", SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List["11000474931", "+", RowBox[List["3613306042", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox["1", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["466821830475", " ", "\[Pi]", " ", SuperscriptBox["z", "2"]]]]]]]]]]

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

 2007-05-02