Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











CoshIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > CoshIntegral[z] > Integration > Indefinite integration > Involving direct function and Gamma-, Beta-, Erf-type functions > Involving exponential integral-type functions and a power function > Involving Si and power





http://functions.wolfram.com/06.40.21.0070.01









  


  










Input Form





Integrate[z^n SinIntegral[b z] CoshIntegral[a z], z] == (1/(4 (1 + n))) (-((1/b) (((ExpIntegralEi[(a - I b) z] + ExpIntegralEi[(-(a + I b)) z] + (-1)^n (ExpIntegralEi[(a + I b) z] + ExpIntegralEi[(-a) z + I b z])) n!)/(I b)^n)) + (1/b) ((2 CoshIntegral[a z] ((-1)^n Gamma[1 + n, (-I) b z] + Gamma[1 + n, I b z]))/(I b)^n) + 4 z^(1 + n) CoshIntegral[a z] SinIntegral[b z] + I a^(-1 - n) n! ((-1)^n ExpIntegralEi[(a - I b) z] - ExpIntegralEi[(-(a + I b)) z] - (-1)^n ExpIntegralEi[(a + I b) z] + ExpIntegralEi[(-a) z + I b z] + (1/(1 + n)!) (2 I (1 + n) ((-1)^n Gamma[1 + n, (-a) z] - Gamma[1 + n, a z]) SinIntegral[b z]) - (-1)^n E^((a - I b) z) Sum[((a/(a - I b))^m Sum[((I b - a)^k z^k)/k!, {k, 0, -1 + m}])/m, {m, 1, n}] + (-1)^n E^((a + I b) z) Sum[((a/(I b + a))^m Sum[((-(I b) - a)^k z^k)/k!, {k, 0, -1 + m}])/m, {m, 1, n}] + Sum[((a/(a + I b))^m Sum[((I b + a)^k z^k)/k!, {k, 0, -1 + m}])/m, {m, 1, n}]/E^((a + I b) z) - E^((-a) z + I b z) Sum[((a/(a - I b))^m Sum[((-(I b) + a)^k z^k)/k!, {k, 0, -1 + m}])/m, {m, 1, n}]) - (1/b) ((2 n! ((-1)^n Sum[(1/(2 k!)) (b^k ((-(I a + b)^(-k)) Gamma[k, (a - I b) z] - Gamma[k, (-(a + I b)) z]/ ((-I) a + b)^k)), {k, 1, n}] + Sum[(1/(2 k!)) (b^k ((-((-I) a + b)^(-k)) Gamma[k, (a + I b) z] - Gamma[k, (-a + I b) z]/(I a + b)^k)), {k, 1, n}]))/(I b)^n)) /; Element[n, Integers] && n >= 0










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "n"], " ", RowBox[List["SinIntegral", "[", RowBox[List["b", " ", "z"]], "]"]], RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["4", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List[FractionBox["1", "b"], RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List["-", "n"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]]]], " ", "z"]], "]"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["(", RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "z"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]], "]"]]]], ")"]]]]]], ")"]], " ", RowBox[List["n", "!"]]]], ")"]]]]]], "+", RowBox[List[FractionBox["1", "b"], RowBox[List["(", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List["-", "n"]]], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["1", "+", "n"]], ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", "z"]]]], "]"]]]], "+", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["1", "+", "n"]], ",", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]], "]"]]]], ")"]]]], ")"]]]], "+", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "+", "n"]]], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["a", RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List["n", "!"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]], "]"]]]], "-", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]]]], " ", "z"]], "]"]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "z"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]], "]"]], "+", RowBox[List[FractionBox["1", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]], "!"]]], RowBox[List["(", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["1", "+", "n"]], ",", RowBox[List[RowBox[List["-", "a"]], " ", "z"]]]], "]"]]]], "-", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["1", "+", "n"]], ",", RowBox[List["a", " ", "z"]]]], "]"]]]], ")"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]], ")"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["a", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]], ")"]], "m"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List[RowBox[List["-", "1"]], "+", "m"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "-", "a"]], ")"]], "k"], " ", SuperscriptBox["z", "k"]]], RowBox[List["k", "!"]]]]]]], "m"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["a", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "a"]]], ")"]], "m"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List[RowBox[List["-", "1"]], "+", "m"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]]]], "-", "a"]], ")"]], "k"], " ", SuperscriptBox["z", "k"]]], RowBox[List["k", "!"]]]]]]], "m"]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]]]], " ", "z"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["a", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]]], ")"]], "m"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List[RowBox[List["-", "1"]], "+", "m"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "a"]], ")"]], "k"], " ", SuperscriptBox["z", "k"]]], RowBox[List["k", "!"]]]]]]], "m"]]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "z"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["a", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]], ")"]], "m"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List[RowBox[List["-", "1"]], "+", "m"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]]]], "+", "a"]], ")"]], "k"], " ", SuperscriptBox["z", "k"]]], RowBox[List["k", "!"]]]]]]], "m"]]]]]]], ")"]]]], "-", RowBox[List[FractionBox["1", "b"], RowBox[List["(", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List["-", "n"]]], " ", RowBox[List["n", "!"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], RowBox[List[FractionBox["1", RowBox[List["2", " ", RowBox[List["k", "!"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["b", "k"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]], RowBox[List["-", "k"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List["k", ",", RowBox[List[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]], RowBox[List["-", "k"]]], " ", RowBox[List["Gamma", "[", RowBox[List["k", ",", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]]]], " ", "z"]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], RowBox[List[FractionBox["1", RowBox[List["2", " ", RowBox[List["k", "!"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["b", "k"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]], RowBox[List["-", "k"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List["k", ",", RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]], RowBox[List["-", "k"]]], " ", RowBox[List["Gamma", "[", RowBox[List["k", ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]], ")"]]]], ")"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mrow> <msup> <mi> z </mi> <mi> n </mi> </msup> <mo> &#8290; </mo> <mrow> <mi> Si </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> Chi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> a </mi> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> Si </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> m </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mn> 1 </mn> <mi> m </mi> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> a </mi> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> </mfrac> <mo> ) </mo> </mrow> <mi> m </mi> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> k </mi> </msup> </mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> m </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mn> 1 </mn> <mi> m </mi> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> a </mi> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> </mfrac> <mo> ) </mo> </mrow> <mi> m </mi> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> k </mi> </msup> </mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> m </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mn> 1 </mn> <mi> m </mi> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> a </mi> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> </mfrac> <mo> ) </mo> </mrow> <mi> m </mi> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> k </mi> </msup> </mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> m </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mn> 1 </mn> <mi> m </mi> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> a </mi> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> </mfrac> <mo> ) </mo> </mrow> <mi> m </mi> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> k </mi> </msup> </mrow> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> - </mo> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> </mrow> <mi> b </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> </msup> </mrow> <mi> b </mi> </mfrac> <mo> &#8290; </mo> <mi> Chi </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> Chi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> Si </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> n </mi> <mo> ! </mo> </mrow> <mtext> </mtext> </mrow> <mi> b </mi> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> b </mi> <mi> k </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> k </mi> </mrow> </msup> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> k </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> b </mi> <mi> k </mi> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> k </mi> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> k </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> k </mi> <mo> , </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> n </ci> </apply> <apply> <ci> SinIntegral </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <ci> CoshIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <factorial /> <ci> n </ci> </apply> <apply> <apply> <power /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <factorial /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <sum /> <bvar> <ci> m </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <ci> k </ci> </apply> <apply> <power /> <ci> z </ci> <ci> k </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <sum /> <bvar> <ci> m </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <ci> k </ci> </apply> <apply> <power /> <ci> z </ci> <ci> k </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <sum /> <bvar> <ci> m </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> <ci> k </ci> </apply> <apply> <power /> <ci> z </ci> <ci> k </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> m </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> m </ci> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <ci> k </ci> </apply> <apply> <power /> <ci> z </ci> <ci> k </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <apply> <factorial /> <ci> n </ci> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <plus /> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> Chi </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> CoshIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <apply> <factorial /> <ci> n </ci> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <factorial /> <ci> k </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <ci> k </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <imaginaryi /> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <ci> k </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> <apply> <ci> Gamma </ci> <ci> k </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <factorial /> <ci> k </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <ci> k </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Gamma </ci> <ci> k </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <imaginaryi /> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> </apply> <apply> <ci> Gamma </ci> <ci> k </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "n_"], " ", RowBox[List["SinIntegral", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List["-", "n"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]]]], " ", "z"]], "]"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["(", RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "z"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]], "]"]]]], ")"]]]]]], ")"]], " ", RowBox[List["n", "!"]]]], "b"]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List["-", "n"]]], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["1", "+", "n"]], ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", "z"]]]], "]"]]]], "+", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["1", "+", "n"]], ",", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]], "]"]]]], ")"]]]], "b"], "+", RowBox[List["4", " ", SuperscriptBox["z", RowBox[List["1", "+", "n"]]], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["a", RowBox[List[RowBox[List["-", "1"]], "-", "n"]]], " ", RowBox[List["n", "!"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]], "]"]]]], "-", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]]]], " ", "z"]], "]"]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "z"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]], "]"]], "+", FractionBox[RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["1", "+", "n"]], ",", RowBox[List[RowBox[List["-", "a"]], " ", "z"]]]], "]"]]]], "-", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["1", "+", "n"]], ",", RowBox[List["a", " ", "z"]]]], "]"]]]], ")"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]], "!"]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["a", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]], ")"]], "m"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List[RowBox[List["-", "1"]], "+", "m"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "-", "a"]], ")"]], "k"], " ", SuperscriptBox["z", "k"]]], RowBox[List["k", "!"]]]]]]], "m"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["a", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "a"]]], ")"]], "m"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List[RowBox[List["-", "1"]], "+", "m"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]]]], "-", "a"]], ")"]], "k"], " ", SuperscriptBox["z", "k"]]], RowBox[List["k", "!"]]]]]]], "m"]]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]]]], " ", "z"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["a", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]]], ")"]], "m"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List[RowBox[List["-", "1"]], "+", "m"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "a"]], ")"]], "k"], " ", SuperscriptBox["z", "k"]]], RowBox[List["k", "!"]]]]]]], "m"]]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "z"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "1"]], "n"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["a", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]]], ")"]], "m"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List[RowBox[List["-", "1"]], "+", "m"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]]]], "+", "a"]], ")"]], "k"], " ", SuperscriptBox["z", "k"]]], RowBox[List["k", "!"]]]]]]], "m"]]]]]]], ")"]]]], "-", FractionBox[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "b"]], ")"]], RowBox[List["-", "n"]]], " ", RowBox[List["n", "!"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], FractionBox[RowBox[List[SuperscriptBox["b", "k"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]], RowBox[List["-", "k"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List["k", ",", RowBox[List[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]], RowBox[List["-", "k"]]], " ", RowBox[List["Gamma", "[", RowBox[List["k", ",", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]]]], " ", "z"]]]], "]"]]]]]], ")"]]]], RowBox[List["2", " ", RowBox[List["k", "!"]]]]]]]]], "+", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "n"], FractionBox[RowBox[List[SuperscriptBox["b", "k"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]], RowBox[List["-", "k"]]]]], " ", RowBox[List["Gamma", "[", RowBox[List["k", ",", RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]], RowBox[List["-", "k"]]], " ", RowBox[List["Gamma", "[", RowBox[List["k", ",", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]]]], "]"]]]]]], ")"]]]], RowBox[List["2", " ", RowBox[List["k", "!"]]]]]]]]], ")"]]]], "b"]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]










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





2001-10-29





© 1998- Wolfram Research, Inc.