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; }

 KelvinKei

 http://functions.wolfram.com/03.15.06.0021.01

 Input Form

 KelvinKei[z] \[Proportional] (I/(E^(((1 + I) z)/Sqrt[2]) (8 Sqrt[2 Pi] Sqrt[(-(-1)^(1/4)) z] ((-1)^(3/4) z)^(3/2)))) (((-Sqrt[(-1)^(3/4) z]) ((-I) E^(I Sqrt[2] z) Pi z + E^(Sqrt[2] z) Pi (4 z - ((1 + I) Sqrt[(-I) z^2])/Sqrt[2]) + 4 ((-E^(I Sqrt[2] z)) z + (-1)^(3/4) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (Log[z] - Log[(-(-1)^(1/4)) z])) + Sqrt[(-(-1)^(1/4)) z] (Pi ((4 - 3 I E^((1 + I) Sqrt[2] z)) z + ((3 - 3 I) Sqrt[I z^2])/ Sqrt[2]) + 4 (E^((1 + I) Sqrt[2] z) z + (-1)^(1/4) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z]))) HypergeometricPFQ[ {1/8, 1/8, 3/8, 3/8, 5/8, 5/8, 7/8, 7/8}, {1/4, 1/2, 3/4}, -(16/z^4)] - ((-1)^(3/4)/(8 z)) ((-(1/2)) Sqrt[(-1)^(3/4) z] (-2 E^(I Sqrt[2] z) Pi z + (1 + I) E^(Sqrt[2] z) Pi ((4 + 4 I) z - I Sqrt[2] Sqrt[(-I) z^2]) + 8 ((-I) E^(I Sqrt[2] z) z + (-1)^(1/4) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z])) + Sqrt[(-(-1)^(1/4)) z] (Pi ((-4 - 3 I E^(2 (-1)^(1/4) z)) z + 3 (-1)^(3/4) Sqrt[I z^2]) + 4 ((-E^((1 + I) Sqrt[2] z)) z + (-1)^(1/4) Sqrt[I z^2]) (Log[z] - Log[(-1)^(3/4) z]))) HypergeometricPFQ[ {3/8, 3/8, 5/8, 5/8, 7/8, 7/8, 9/8, 9/8}, {1/2, 3/4, 5/4}, -(16/z^4)] - ((9 I)/(128 z^2)) (Sqrt[(-1)^(3/4) z] ((-I) E^(I Sqrt[2] z) Pi z + E^(Sqrt[2] z) Pi (4 z - ((1 + I) Sqrt[(-I) z^2])/Sqrt[2]) + 4 ((-E^(I Sqrt[2] z)) z + (-1)^(3/4) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (Log[z] - Log[(-(-1)^(1/4)) z])) + Sqrt[(-(-1)^(1/4)) z] (Pi ((4 - 3 I E^((1 + I) Sqrt[2] z)) z + ((3 - 3 I) Sqrt[I z^2])/ Sqrt[2]) + 4 (E^((1 + I) Sqrt[2] z) z + (-1)^(1/4) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z]))) HypergeometricPFQ[ {5/8, 5/8, 7/8, 7/8, 9/8, 9/8, 11/8, 11/8}, {3/4, 5/4, 3/2}, -(16/z^4)] - ((75 (-1)^(1/4))/(1024 z^3)) ((1/2) Sqrt[(-1)^(3/4) z] (-2 E^(I Sqrt[2] z) Pi z + (1 + I) E^(Sqrt[2] z) Pi ((4 + 4 I) z - I Sqrt[2] Sqrt[(-I) z^2]) + 8 ((-I) E^(I Sqrt[2] z) z + (-1)^(1/4) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z])) + Sqrt[(-(-1)^(1/4)) z] (Pi ((-4 - 3 I E^(2 (-1)^(1/4) z)) z + 3 (-1)^(3/4) Sqrt[I z^2]) + 4 ((-E^((1 + I) Sqrt[2] z)) z + (-1)^(1/4) Sqrt[I z^2]) (Log[z] - Log[(-1)^(3/4) z]))) HypergeometricPFQ[ {7/8, 7/8, 9/8, 9/8, 11/8, 11/8, 13/8, 13/8}, {5/4, 3/2, 7/4}, -(16/z^4)]) /; (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinKei", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], SqrtBox["2"]]]]]]], RowBox[List["8", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", "z"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "z"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]], SqrtBox["2"]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["4", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]]]]]], ")"]], " ", "z"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "-", RowBox[List["3", " ", "\[ImaginaryI]"]]]], ")"]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]], SqrtBox["2"]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "8"], ",", FractionBox["1", "8"], ",", FractionBox["3", "8"], ",", FractionBox["3", "8"], ",", FractionBox["5", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"], ",", FractionBox["7", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " "]], RowBox[List["8", " ", "z"]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["4", "+", RowBox[List["4", " ", "\[ImaginaryI]"]]]], ")"]], " ", "z"]], "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]]]], "+", RowBox[List["8", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "8"], ",", FractionBox["3", "8"], ",", FractionBox["5", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"], ",", FractionBox["7", "8"], ",", FractionBox["9", "8"], ",", FractionBox["9", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "4"], ",", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["9", "\[ImaginaryI]"]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", "z"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "z"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]], SqrtBox["2"]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["4", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]]]]]], ")"]], " ", "z"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "-", RowBox[List["3", " ", "\[ImaginaryI]"]]]], ")"]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]], SqrtBox["2"]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"], ",", FractionBox["7", "8"], ",", FractionBox["9", "8"], ",", FractionBox["9", "8"], ",", FractionBox["11", "8"], ",", FractionBox["11", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["5", "4"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["75", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " "]], RowBox[List["1024", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["4", "+", RowBox[List["4", " ", "\[ImaginaryI]"]]]], ")"]], " ", "z"]], "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]]]], "+", RowBox[List["8", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["7", "8"], ",", FractionBox["7", "8"], ",", FractionBox["9", "8"], ",", FractionBox["9", "8"], ",", FractionBox["11", "8"], ",", FractionBox["11", "8"], ",", FractionBox["13", "8"], ",", FractionBox["13", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "4"], ",", FractionBox["3", "2"], ",", FractionBox["7", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]

 MathML Form

 kei ( z ) - ( 1 + ) z 2 8 2 π - - 1 4 z ( ( - 1 ) 3 / 4 z ) 3 / 2 ( ( - - 1 4 z ( π ( z 2 ( 3 - 3 ) 2 + ( 4 - 3 ( 1 + ) 2 z ) z ) + 4 ( ( 1 + ) 2 z z + - 1 4 z 2 ) ( log ( ( - 1 ) 3 / 4 z ) - log ( z ) ) ) - ( - 1 ) 3 / 4 z ( 2 z π ( 4 z - ( 1 + ) - z 2 2 ) + 2 z ( - ) π z + 4 ( ( - 1 ) 3 / 4 2 z - z 2 - 2 z z ) ( log ( z ) - log ( - - 1 4 z ) ) ) ) 8 F 3 ( 1 8 , 1 8 , 3 8 , 3 8 , 5 8 , 5 8 , 7 8 , 7 8 ; 1 4 , 1 2 , 3 4 ; - 16 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] - ( - 1 ) 3 / 4 8 z ( - - 1 4 z ( π ( ( - 4 - 3 2 - 1 4 z ) z + 3 ( - 1 ) 3 / 4 z 2 ) + 4 ( - 1 4 z 2 - ( 1 + ) 2 z z ) ( log ( z ) - log ( ( - 1 ) 3 / 4 z ) ) ) - 1 2 ( - 1 ) 3 / 4 z ( - 2 2 z π z + 2 z ( 1 + ) π ( ( 4 + 4 ) z - 2 - z 2 ) + 8 ( - 1 4 2 z - z 2 - 2 z z ) ( log ( - - 1 4 z ) - log ( z ) ) ) ) 8 F 3 ( 3 8 , 3 8 , 5 8 , 5 8 , 7 8 , 7 8 , 9 8 , 9 8 ; 1 2 , 3 4 , 5 4 ; - 16 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] - 9 128 z 2 ( ( - 1 ) 3 / 4 z ( 2 z π ( 4 z - ( 1 + ) - z 2 2 ) + 2 z ( - ) π z + 4 ( ( - 1 ) 3 / 4 2 z - z 2 - 2 z z ) ( log ( z ) - log ( - - 1 4 z ) ) ) + - - 1 4 z ( π ( z 2 ( 3 - 3 ) 2 + ( 4 - 3 ( 1 + ) 2 z ) z ) + 4 ( ( 1 + ) 2 z z + - 1 4 z 2 ) ( log ( ( - 1 ) 3 / 4 z ) - log ( z ) ) ) ) 8 F 3 ( 5 8 , 5 8 , 7 8 , 7 8 , 9 8 , 9 8 , 11 8 , 11 8 ; 3 4 , 5 4 , 3 2 ; - 16 z 4 ) - 75 - 1 4 1024 z 3 ( 1 2 ( - 1 ) 3 / 4 z ( - 2 2 z π z + 2 z ( 1 + ) π ( ( 4 + 4 ) z - 2 - z 2 ) + 8 ( - 1 4 2 z - z 2 - 2 z z ) ( log ( - - 1 4 z ) - log ( z ) ) ) + - - 1 4 z ( π ( ( - 4 - 3 2 - 1 4 z ) z + 3 ( - 1 ) 3 / 4 z 2 ) + 4 ( - 1 4 z 2 - ( 1 + ) 2 z z ) ( log ( z ) - log ( ( - 1 ) 3 / 4 z ) ) ) ) 8 F 3 ( 7 8 , 7 8 , 9 8 , 9 8 , 11 8 , 11 8 , 13 8 , 13 8 ; 5 4 , 3 2 , 7 4 ; - 16 z 4 ) TagBox[RowBox[List[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], "-", RowBox[List[FractionBox[RowBox[List["75", " ", RadicalBox[RowBox[List["-", "1"]], "4"]]], RowBox[List["1024", " ", SuperscriptBox["z", "3"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", "z"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["4", "+", RowBox[List["4", " ", "\[ImaginaryI]"]]]], ")"]], " ", "z"]], "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]]]], "+", RowBox[List["8", " ", RowBox[List["(", RowBox[List[RowBox[List[RadicalBox[RowBox[List["-", "1"]], "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "z"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["log", "(", RowBox[List[RowBox[List["-", RadicalBox[RowBox[List["-", "1"]], "4"]]], " ", "z"]], ")"]], "-", RowBox[List["log", "(", "z", ")"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", RadicalBox[RowBox[List["-", "1"]], "4"]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", RadicalBox[RowBox[List["-", "1"]], "4"], " ", "z"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RadicalBox[RowBox[List["-", "1"]], "4"], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]], " ", "z"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["log", "(", "z", ")"]], "-", RowBox[List["log", "(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], ")"]]]], ")"]]]]]], ")"]]]]]], ")"]], TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["13", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["13", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ], " "]]]], HypergeometricPFQ] ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional KelvinKei z -1 1 z 2 1 2 -1 8 2 1 2 -1 -1 1 4 z 1 2 -1 3 4 z 3 2 -1 -1 -1 1 4 z 1 2 z 2 1 2 3 -3 2 1 2 -1 4 -1 3 1 2 1 2 z z 4 1 2 1 2 z z -1 1 4 z 2 1 2 -1 3 4 z -1 z -1 -1 3 4 z 1 2 2 1 2 z 4 z -1 1 -1 z 2 1 2 2 1 2 -1 2 1 2 z -1 z 4 -1 3 4 2 1 2 z -1 z 2 1 2 -1 2 1 2 z z z -1 -1 -1 1 4 z HypergeometricPFQ 1 8 1 8 3 8 3 8 5 8 5 8 7 8 7 8 1 4 1 2 3 4 -1 16 z 4 -1 -1 -1 3 4 8 z -1 -1 -1 1 4 z 1 2 -4 -1 3 2 -1 1 4 z z 3 -1 3 4 z 2 1 2 4 -1 1 4 z 2 1 2 -1 1 2 1 2 z z z -1 -1 3 4 z -1 1 2 -1 3 4 z 1 2 -2 2 1 2 z z 2 1 2 z 1 4 4 z -1 2 1 2 -1 z 2 1 2 8 -1 1 4 2 1 2 z -1 z 2 1 2 -1 2 1 2 z z -1 -1 1 4 z -1 z HypergeometricPFQ 3 8 3 8 5 8 5 8 7 8 7 8 9 8 9 8 1 2 3 4 5 4 -1 16 z 4 -1 -1 9 128 z 2 -1 -1 3 4 z 1 2 2 1 2 z 4 z -1 1 -1 z 2 1 2 2 1 2 -1 2 1 2 z -1 z 4 -1 3 4 2 1 2 z -1 z 2 1 2 -1 2 1 2 z z z -1 -1 -1 1 4 z -1 -1 1 4 z 1 2 z 2 1 2 3 -3 2 1 2 -1 4 -1 3 1 2 1 2 z z 4 1 2 1 2 z z -1 1 4 z 2 1 2 -1 3 4 z -1 z HypergeometricPFQ HypergeometricPFQ 5 8 5 8 7 8 7 8 9 8 9 8 11 8 11 8 3 4 5 4 3 2 -1 16 z 4 -1 -1 75 -1 1 4 1024 z 3 -1 1 2 -1 3 4 z 1 2 -2 2 1 2 z z 2 1 2 z 1 4 4 z -1 2 1 2 -1 z 2 1 2 8 -1 1 4 2 1 2 z -1 z 2 1 2 -1 2 1 2 z z -1 -1 1 4 z -1 z -1 -1 1 4 z 1 2 -4 -1 3 2 -1 1 4 z z 3 -1 3 4 z 2 1 2 4 -1 1 4 z 2 1 2 -1 1 2 1 2 z z z -1 -1 3 4 z HypergeometricPFQ 7 8 7 8 9 8 9 8 11 8 11 8 13 8 13 8 5 4 3 2 7 4 -1 16 z 4 -1 Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKei", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], SqrtBox["2"]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", "z"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "z"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]], SqrtBox["2"]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["4", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]]]]]], ")"]], " ", "z"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "-", RowBox[List["3", " ", "\[ImaginaryI]"]]]], ")"]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]], SqrtBox["2"]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "8"], ",", FractionBox["1", "8"], ",", FractionBox["3", "8"], ",", FractionBox["3", "8"], ",", FractionBox["5", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"], ",", FractionBox["7", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["4", "+", RowBox[List["4", " ", "\[ImaginaryI]"]]]], ")"]], " ", "z"]], "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]]]], "+", RowBox[List["8", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "8"], ",", FractionBox["3", "8"], ",", FractionBox["5", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"], ",", FractionBox["7", "8"], ",", FractionBox["9", "8"], ",", FractionBox["9", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "4"], ",", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], RowBox[List["8", " ", "z"]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["9", " ", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", "z"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "z"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]], SqrtBox["2"]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["4", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]]]]]], ")"]], " ", "z"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "-", RowBox[List["3", " ", "\[ImaginaryI]"]]]], ")"]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]], SqrtBox["2"]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"], ",", FractionBox["7", "8"], ",", FractionBox["9", "8"], ",", FractionBox["9", "8"], ",", FractionBox["11", "8"], ",", FractionBox["11", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["5", "4"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["75", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["4", "+", RowBox[List["4", " ", "\[ImaginaryI]"]]]], ")"]], " ", "z"]], "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]]]], "+", RowBox[List["8", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "4"]], "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["7", "8"], ",", FractionBox["7", "8"], ",", FractionBox["9", "8"], ",", FractionBox["9", "8"], ",", FractionBox["11", "8"], ",", FractionBox["11", "8"], ",", FractionBox["13", "8"], ",", FractionBox["13", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "4"], ",", FractionBox["3", "2"], ",", FractionBox["7", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], RowBox[List["1024", " ", SuperscriptBox["z", "3"]]]]]], ")"]]]], RowBox[List["8", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]

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

 2007-05-02