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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and a power functions > Involving powers of sinh and power > Involving zalpha-1 sinhm(b zr+e) cosh(c zr+g)





http://functions.wolfram.com/01.20.21.1777.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) Sinh[b z^r + e]^m Cosh[c z^r + g], z] == 2^(-1 - m) z^\[Alpha] ((1/r) ((Binomial[m, m/2] ((E^g Gamma[\[Alpha]/r, (-c) z^r])/ ((-c) z^r)^(\[Alpha]/r) + Gamma[\[Alpha]/r, c z^r]/ (E^g (c z^r)^(\[Alpha]/r))) (-1 + Mod[m, 2]))/I^m) - (1/r) Sum[(-1)^k E^(-g + 2 e k - e m) Binomial[m, k] ((E^(2 g - 4 e k + 2 e m) Gamma[\[Alpha]/r, (-c + 2 b k - b m) z^r])/ ((-c + 2 b k - b m) z^r)^(\[Alpha]/r) + (E^(-4 e k + 2 e m) Gamma[\[Alpha]/r, (c + 2 b k - b m) z^r])/ ((c + 2 b k - b m) z^r)^(\[Alpha]/r) + ((-1)^m E^(2 g) Gamma[\[Alpha]/r, (-c - 2 b k + b m) z^r])/ ((-c - 2 b k + b m) z^r)^(\[Alpha]/r) + ((-1)^m Gamma[\[Alpha]/r, (c - 2 b k + b m) z^r])/ ((c - 2 b k + b m) z^r)^(\[Alpha]/r)), {k, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0










Standard Form





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MathML Form







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</ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <imaginaryi /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <ci> g </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> g </ci> </apply> </apply> <apply> <power /> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; 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</ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> g </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> e </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#945; 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Rule Form





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





2002-12-18