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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power > Involving zn eb zr+e cosh(f z+g)





http://functions.wolfram.com/01.20.21.0366.01









  


  










Input Form





Integrate[z^n E^(b z^2 + e) Cosh[f z + g], z] == (-(1/4)) b^(-1 - n) (E^(e - f^2/(4 b) - g) Sum[2^(-n + q) f^(n - q) (-f + 2 b z)^(1 + q) (-((-f + 2 b z)^2/b))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((-f + 2 b z)^2/(4 b))], {q, 0, n}] + E^(e - f^2/(4 b) + g) Sum[2^(-n + q) (-f)^(n - q) (f + 2 b z)^(1 + q) (-((f + 2 b z)^2/b))^ ((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((f + 2 b z)^2/(4 b))], {q, 0, n}]) /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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<apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> q </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> f </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18