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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving polynomials or algebraic functions and factors involving exponential function and a power function > Involving exp and power > Involving zn ed z cosh(c zr+f z+g)





http://functions.wolfram.com/01.20.21.0513.01









  


  










Input Form





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










Standard Form





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MathML Form







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<apply> <ci> Binomial </ci> <ci> n </ci> <ci> q </ci> </apply> <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> d </ci> <ci> f </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </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