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Csch






Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic and trigonometric functions > Involving powers of the direct function, hyperbolic and trigonometric functions > Involving cos and sinh > Involving cos(a z)sinh(b z) cschv( c z)





http://functions.wolfram.com/01.23.21.0506.01









  


  










Input Form





Integrate[Cos[a z] Sinh[b z] Csch[c z]^\[Nu], z] == (2^(-2 + \[Nu]) E^(z (I a + b - c \[Nu])) (E^((-I) a z) + E^(I a z)) (-E^((-b) z) + E^(b z)) (1 - E^(2 c z))^\[Nu] (E^(c z)/(-1 + E^(2 c z)))^ \[Nu] ((1/(I a + b - c \[Nu])) (E^(z ((-I) a - b + c \[Nu])) Hypergeometric2F1[-((I a + b - c \[Nu])/(2 c)), \[Nu], -((I a + b - c (2 + \[Nu]))/(2 c)), E^(2 c z)]) + (1/((-I) a + b - c \[Nu])) (E^(z (I a - b + c \[Nu])) Hypergeometric2F1[(I a - b + c \[Nu])/(2 c), \[Nu], (I a - b + c (2 + \[Nu]))/(2 c), E^(2 c z)]) + I ((1/(a + I (b + c \[Nu]))) (E^(z ((-I) a + b + c \[Nu])) Hypergeometric2F1[((-I) a + b + c \[Nu])/(2 c), \[Nu], ((-I) a + b + c (2 + \[Nu]))/(2 c), E^(2 c z)]) - (1/(a - I (b + c \[Nu]))) (E^(z (I a + b + c \[Nu])) Hypergeometric2F1[(I a + b + c \[Nu])/(2 c), \[Nu], (I a + b + c (2 + \[Nu]))/(2 c), E^(2 c z)]))))/ ((1 + E^(2 I a z)) (-1 + E^(2 b z)))










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