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SinhIntegral






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.39.21.0064.01









  


  










Input Form





Integrate[z^n ExpIntegralEi[a z] SinhIntegral[a z], z] == (1/(n + 1)) (z^(1 + n) ExpIntegralEi[a z] + (-a)^(-1 - n) Gamma[1 + n, (-a) z]) SinhIntegral[a z] - (a^(-1 - n)/(2 (1 + n))) (((-1)^n Gamma[1 + n, (-a) z] + Gamma[1 + n, a z]) ExpIntegralEi[a z] - (-1)^n n! ExpIntegralEi[2 a z] - n! Log[z] + (-1)^n n! Sum[Gamma[k, -2 a z]/(2^k k!), {k, 1, n}] - n! Sum[(a z)^k/(k k!), {k, 1, n}]) - (((-a)^(-1 - n) n!)/(2 (1 + n))) (ExpIntegralEi[2 a z] - Log[z] - Sum[(((-a) z)^k/k + Gamma[k, -2 a z]/2^k)/k!, {k, 1, n}]) /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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</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> <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> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29