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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric, exponential and a power functions > Involving powers of the direct function, trigonometric, exponential and a power functions > Involving cos, exp and power > Involving zalpha-1ep zcos(c z+d)coshnu(a z+b)





http://functions.wolfram.com/01.20.21.3970.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) E^(p z) Cos[d + c z] Cosh[b + a z]^v, z] == 2^(-1 - v) z^\[Alpha] ((Binomial[v, v/2] (E^(2 I d) ExpIntegralE[1 - \[Alpha], ((-I) c - p) z] + ExpIntegralE[1 - \[Alpha], (I c - p) z]) (-1 + Mod[v, 2]))/E^(I d) - Sum[E^((-I) d - b (2 s + v)) Binomial[v, s] (E^(2 b v) ExpIntegralE[1 - \[Alpha], (I c - p + 2 a s - a v) z] + E^(2 I d) (E^(2 b v) ExpIntegralE[1 - \[Alpha], ((-I) c - p + 2 a s - a v) z] + E^(4 b s) ExpIntegralE[ 1 - \[Alpha], ((-I) c - p - 2 a s + a v) z]) + E^(4 b s) ExpIntegralE[1 - \[Alpha], (I c - p - 2 a s + a v) z]), {s, 0, Floor[(1/2) (-1 + v)]}]) /; Element[v, Integers] && v > 0










Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <ci> v </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> v </ci> </apply> </apply> <apply> <ci> ExpIntegralE </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> v </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> <ci> s </ci> </apply> </apply> <apply> <ci> ExpIntegralE </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; 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Rule Form





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





2002-12-18