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Coth




Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and trigonometric functions > Involving sin and cosh > Involving sin(a z)cosh(b z) coth( c z)





http://functions.wolfram.com/01.22.21.0180.01









  


  








Input Form





Integrate[Sin[a z] Cosh[b z] Coth[c z], z] == (1/4) I (-((E^(((-I) a - b) z) Hypergeometric2F1[((-I) a - b)/(2 c), 1, ((-I) a - b + 2 c)/(2 c), E^(2 c z)])/((-I) a - b)) + (E^((I a - b) z) Hypergeometric2F1[(I a - b)/(2 c), 1, (I a - b + 2 c)/(2 c), E^(2 c z)])/(I a - b) - (E^(((-I) a + b) z) Hypergeometric2F1[((-I) a + b)/(2 c), 1, ((-I) a + b + 2 c)/(2 c), E^(2 c z)])/((-I) a + b) + (E^((I a + b) z) Hypergeometric2F1[(I a + b)/(2 c), 1, (I a + b + 2 c)/(2 c), E^(2 c z)])/(I a + b) - (E^(((-I) a - b + 2 c) z) Hypergeometric2F1[((-I) a - b + 2 c)/(2 c), 1, ((-I) a - b + 4 c)/(2 c), E^(2 c z)])/((-I) a - b + 2 c) + (E^((I a - b + 2 c) z) Hypergeometric2F1[(I a - b + 2 c)/(2 c), 1, (I a - b + 4 c)/(2 c), E^(2 c z)])/(I a - b + 2 c) - (E^(((-I) a + b + 2 c) z) Hypergeometric2F1[((-I) a + b + 2 c)/(2 c), 1, ((-I) a + b + 4 c)/(2 c), E^(2 c z)])/((-I) a + b + 2 c) + (E^((I a + b + 2 c) z) Hypergeometric2F1[(I a + b + 2 c)/(2 c), 1, (I a + b + 4 c)/(2 c), E^(2 c z)])/(I a + b + 2 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