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.aje3.01

 Input Form

 Hypergeometric2F1[1, 2, 1/4, z] == (1/(32 (1 - z)^(11/4))) (32 (1 - z)^(3/4) + 24 (1 - z)^(3/4) z - 42 Sqrt[2] z^(3/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 42 Sqrt[2] z^(3/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 21 Sqrt[2] z^(3/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 21 Sqrt[2] z^(3/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "2", ",", FractionBox["1", "4"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["32", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["11", "/", "4"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["32", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]], "+", RowBox[List["24", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "-", RowBox[List["42", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], "-", RowBox[List["42", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], "-", RowBox[List["21", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], "+", RowBox[List["21", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 1 , 2 ; 1 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["1", "4"], 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 32 ( 1 - z ) 11 / 4 ( 24 ( 1 - z ) 3 / 4 z - 42 2 tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) z 3 / 4 - 42 2 tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) z 3 / 4 - 21 2 log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) z 3 / 4 + 21 2 log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) z 3 / 4 + 32 ( 1 - z ) 3 / 4 ) HypergeometricPFQ 1 2 1 4 z 1 32 1 -1 z 11 4 -1 24 1 -1 z 3 4 z -1 42 2 1 2 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 z 3 4 -1 42 2 1 2 z 1 4 2 1 2 1 -1 z 1 4 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 z 3 4 -1 21 2 1 2 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 3 4 21 2 1 2 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 3 4 32 1 -1 z 3 4 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "2", ",", FractionBox["1", "4"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["32", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]]]], "+", RowBox[List["24", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "-", RowBox[List["42", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], "-", RowBox[List["42", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["1", "+", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", RowBox[List["1", "/", "4"]]], RowBox[List[SqrtBox["2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]]]]]]]], "]"]]]], "-", RowBox[List["21", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]], "+", RowBox[List["21", " ", SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]]], "+", FractionBox[SqrtBox["z"], SqrtBox[RowBox[List["1", "-", "z"]]]]]], "]"]]]]]], RowBox[List["32", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["11", "/", "4"]]]]]]]]]]

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

 2007-05-02