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Erfc






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfc[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions and a power function > Involving cos and power





http://functions.wolfram.com/06.27.21.0041.01









  


  










Input Form





Integrate[z^n Cos[b z] Erfc[a z], z] == (I/2) b^(-1 - n) (I^n Erfc[a z] (-Gamma[1 + n, (-I) b z] + (-1)^n Gamma[1 + n, I b z]) + ((a n!)/Sqrt[Pi]) Exp[-(b^2/(4 a^2))] ((-(-I)^n) Sum[((I b)^m/m!) (-a^2)^((1/2) (-1 - m)) Sum[Binomial[m, k] (-(((-I) b)/(2 Sqrt[-a^2])))^(m - k) (Sqrt[-a^2] z - (I b)/(2 Sqrt[-a^2]))^(1 + k) (-(Sqrt[-a^2] z - (I b)/(2 Sqrt[-a^2]))^2)^((1/2) (-1 - k)) Gamma[(1 + k)/2, -(Sqrt[-a^2] z - (I b)/(2 Sqrt[-a^2]))^2], {k, 0, m}], {m, 0, n}] + I^n Sum[(((-I) b)^m/m!) (-a^2)^((1/2) (-1 - m)) Sum[Binomial[m, k] (-((I b)/(2 Sqrt[-a^2])))^(m - k) (Sqrt[-a^2] z + (I b)/(2 Sqrt[-a^2]))^(1 + k) (-(Sqrt[-a^2] z + (I b)/(2 Sqrt[-a^2]))^2)^((1/2) (-1 - k)) Gamma[(1 + k)/2, -(Sqrt[-a^2] z + (I b)/(2 Sqrt[-a^2]))^2], {k, 0, m}], {m, 0, n}])) /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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





2001-10-29





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