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Coth






Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving sin and exp > Involving ep z sin(b z)





http://functions.wolfram.com/01.22.21.0051.01









  


  










Input Form





Integrate[(Sin[a z] Coth[c z])/E^((I b + 2 c) z), z] == (1/2) ((E^(I (a - b) z) Hypergeometric2F1[(I (a - b))/(2 c), 1, 1 + (I (a - b))/(2 c), E^(2 c z)])/(a - b) + Hypergeometric2F1[-((I (a + b))/(2 c)), 1, 1 - (I (a + b))/(2 c), E^(2 c z)]/(E^(I (a + b) z) (a + b)) + (1/(a + b - 2 I c)) (Hypergeometric2F1[-((I (a + b - 2 I c))/(2 c)), 1, -((I (a + b))/(2 c)), E^(2 c z)]/E^(I (a + b - 2 I c) z)) + (E^(I (a - b + 2 I c) z) Hypergeometric2F1[(I (a - b + 2 I c))/(2 c), 1, (I (a - b))/(2 c), E^(2 c z)])/(a - b + 2 I c))










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)





2002-12-18