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.c0cn.01

 Input Form

 Hypergeometric2F1[5/8, 5, 21/8, z] == (1/6291456) (65 (-((64 (1059 - 1558 z + 627 z^2))/(-1 + z)^3) - (1/z^(13/8)) (627 (8 z^(5/8) + 5 Log[1 - z^(1/8)] - 5 I Log[1 - I z^(1/8)] + 5 I Log[1 + I z^(1/8)] - 5 Log[1 + z^(1/8)] + 5 (-1)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] - 5 (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] + 5 (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] - 5 (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)])) - (1/z^(5/8)) (16929 (Log[1 - z^(1/8)] - I Log[1 - I z^(1/8)] + I Log[1 + I z^(1/8)] - Log[1 + z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)]))))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "8"], ",", "5", ",", FractionBox["21", "8"], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "6291456"], RowBox[List["(", RowBox[List["65", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["64", " ", RowBox[List["(", RowBox[List["1059", "-", RowBox[List["1558", " ", "z"]], "+", RowBox[List["627", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "3"]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox["z", RowBox[List["13", "/", "8"]]]], RowBox[List["(", RowBox[List["627", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", SuperscriptBox["z", RowBox[List["5", "/", "8"]]]]], "+", RowBox[List["5", " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]], "]"]]]], "-", RowBox[List["5", " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["5", " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["5", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]], "]"]]]], "+", RowBox[List["5", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["5", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["5", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["5", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]]]], ")"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox["z", RowBox[List["5", "/", "8"]]]], RowBox[List["(", RowBox[List["16929", " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]], "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]], "]"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 5 8 , 5 ; 21 8 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["21", "8"], 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 6291456 ( 65 ( - 64 ( 627 z 2 - 1558 z + 1059 ) ( z - 1 ) 3 - 1 z 13 / 8 ( 627 ( 5 log ( 1 - z 8 ) - 5 log ( 1 - z 8 ) + 5 log ( z 8 + 1 ) - 5 log ( z 8 + 1 ) + 5 ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) - 5 ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) + 5 - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 5 - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 8 z 5 / 8 ) ) - 1 z 5 / 8 ( 16929 ( log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) - log ( z 8 + 1 ) + ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) - ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) ) ) HypergeometricPFQ 5 8 5 21 8 z 1 6291456 65 -1 64 627 z 2 -1 1558 z 1059 z -1 3 -1 -1 1 z 13 8 -1 627 5 1 -1 z 1 8 -1 5 1 -1 z 1 8 5 z 1 8 1 -1 5 z 1 8 1 5 -1 3 4 1 -1 -1 1 4 z 1 8 -1 5 -1 3 4 -1 1 4 z 1 8 1 5 -1 1 4 1 -1 -1 3 4 z 1 8 -1 5 -1 1 4 -1 3 4 z 1 8 1 8 z 5 8 -1 1 z 5 8 -1 16929 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 -1 z 1 8 1 -1 3 4 1 -1 -1 1 4 z 1 8 -1 -1 3 4 -1 1 4 z 1 8 1 -1 1 4 1 -1 -1 3 4 z 1 8 -1 -1 1 4 -1 3 4 z 1 8 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["5", "8"], ",", "5", ",", FractionBox["21", "8"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["65", " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["64", " ", RowBox[List["(", RowBox[List["1059", "-", RowBox[List["1558", " ", "z"]], "+", RowBox[List["627", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "3"]]]], "-", FractionBox[RowBox[List["627", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", SuperscriptBox["z", RowBox[List["5", "/", "8"]]]]], "+", RowBox[List["5", " ", RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]], "]"]]]], "-", RowBox[List["5", " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["5", " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["5", " ", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]], "]"]]]], "+", RowBox[List["5", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["5", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["5", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["5", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]]]], ")"]]]], SuperscriptBox["z", RowBox[List["13", "/", "8"]]]], "-", FractionBox[RowBox[List["16929", " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]], "]"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List["Log", "[", RowBox[List["1", "+", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]], "]"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["z", RowBox[List["1", "/", "8"]]]]]]], "]"]]]]]], ")"]]]], SuperscriptBox["z", RowBox[List["5", "/", "8"]]]]]], ")"]]]], "6291456"]]]]]

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

 2007-05-02