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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function and exponential function > Involving products of powers of two direct functions and exponential function > Involving products of powers of two direct functions and exponential function > Involving ep zcoshmu(c z) coshv(a z+b)





http://functions.wolfram.com/01.20.21.2836.01









  


  








Input Form





Integrate[E^(p z) Cosh[c z]^\[Mu] Cosh[b + a z]^v, z] == (Binomial[v, v/2] (1 - Mod[v, 2]) (1/(p - c \[Mu])) ((E^(p z) Cosh[c z]^\[Mu] Hypergeometric2F1[(p - c \[Mu])/(2 c), -\[Mu], (1/2) (2 + p/c - \[Mu]), -E^(2 c z)])/(1 + E^(2 c z))^\[Mu]))/2^v + Sum[(Binomial[v, s] Cosh[c z]^\[Mu] (-(E^((p - a (-2 s + v)) z) Hypergeometric2F1[ -((p - a (-2 s + v) + c \[Mu])/(2 c)), -\[Mu], (1/2) (2 + (-p + a (-2 s + v))/c - \[Mu]), -E^(-2 c z)])/ (-p + a (-2 s + v) - c \[Mu]) + (E^(2 b (-2 s + v) + (p + a (-2 s + v)) z) Hypergeometric2F1[ -((p + a (-2 s + v) + c \[Mu])/(2 c)), -\[Mu], -((p + a (-2 s + v) + c (-2 + \[Mu]))/(2 c)), -E^(-2 c z)])/ (p + a (-2 s + v) + c \[Mu])))/(E^(b (-2 s + v)) (1 + E^(-2 c z))^\[Mu]), {s, 0, Floor[(1/2) (-1 + v)]}]/2^v /; Element[v, Integers] && v > 0








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