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ExpIntegralEi






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > ExpIntegralEi[z] > Integration > Indefinite integration > Involving functions of the direct function and elementary functions > Involving elementary functions of the direct function and elementary functions > Involving products of the direct function and a power function





http://functions.wolfram.com/06.35.21.0063.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





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





2001-10-29