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Erfi






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erfi[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power, exponential and trigonometric functions > Involving power, exp and sin





http://functions.wolfram.com/06.28.21.0058.01









  


  










Input Form





Integrate[z^2 E^(b z) Sin[c z] Erfi[a z], z] == (1/(8 a^4 Sqrt[Pi])) (I E^(a^2 z^2) ((1/(b - I c)^3) (2 a (b - I c) E^((b - I c) z) ((b - I c)^2 + a^2 (4 - 2 b z + 2 I c z)) + 4 a^4 E^(z (b - I c - a^2 z)) Sqrt[Pi] (2 - 2 (b - I c) z + (b - I c)^2 z^2) Erfi[a z] - (8 a^4 + 2 a^2 (b - I c)^2 + (b - I c)^4) E^(-((b - I c)^2/(4 a^2)) - a^2 z^2) Sqrt[Pi] Erfi[(b - I c)/(2 a) + a z]) - (1/(b + I c)^3) (2 a (b + I c) E^((b + I c) z) ((b + I c)^2 - 2 a^2 (-2 + b z + I c z)) + 4 a^4 E^(z (b + I c - a^2 z)) Sqrt[Pi] (2 - 2 (b + I c) z + (b + I c)^2 z^2) Erfi[a z] - (8 a^4 + 2 a^2 (b + I c)^2 + (b + I c)^4) E^(-((b + I c)^2/(4 a^2)) - a^2 z^2) Sqrt[Pi] Erfi[(b + I c)/(2 a) + a z])))










Standard Form





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Rule Form





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





2001-10-29