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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and a power functions > Involving cos and power > Involving zalpha-1cos(c z+d)cosh(a z+b)





http://functions.wolfram.com/01.20.21.1035.01









  


  








Input Form





Integrate[z^(\[Alpha] - 1) Cos[d + c z] Cosh[b + a z], z] == ((-(1/4)) z^\[Alpha] (((-(a - I c)) z)^\[Alpha] ((-(a + I c)^2) z^2)^ \[Alpha] Gamma[\[Alpha], (a - I c) z] (Cos[d] + I Sin[d]) (Cosh[b] - Sinh[b]) + ((a - I c) z)^\[Alpha] ((-(a + I c)^2) z^2)^ \[Alpha] Gamma[\[Alpha], (-(a - I c)) z] (Cos[d] - I Sin[d]) (Cosh[b] + Sinh[b]) + ((-(a - I c)^2) z^2)^\[Alpha] (((-(a + I c)) z)^\[Alpha] Gamma[\[Alpha], (a + I c) z] (Cos[d] - I Sin[d]) (Cosh[b] - Sinh[b]) + ((a + I c) z)^\[Alpha] Gamma[\[Alpha], (-(a + I c)) z] (Cos[d] + I Sin[d]) (Cosh[b] + Sinh[b]))))/(((-(a - I c)^2) z^2)^\[Alpha] ((-(a + I c)^2) z^2)^\[Alpha])








Standard Form





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MathML Form







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</ci> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> </apply> <ci> z </ci> </apply> <ci> &#945; </ci> </apply> <apply> <ci> Gamma </ci> <ci> &#945; </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <cos /> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <sin /> <ci> d </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <cosh /> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sinh /> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#945; </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <ci> z </ci> </apply> <ci> &#945; </ci> </apply> <apply> <ci> Gamma </ci> <ci> &#945; </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <cos /> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <sin /> <ci> d </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <cosh /> <ci> b </ci> </apply> <apply> <sinh /> <ci> b </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#945; </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#945; </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Gamma </ci> <ci> &#945; </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <cos /> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <sin /> <ci> d </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <cosh /> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <sinh /> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <ci> z </ci> </apply> <ci> &#945; </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <ci> z </ci> </apply> <ci> &#945; </ci> </apply> <apply> <ci> Gamma </ci> <ci> &#945; </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <cos /> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <sin /> <ci> d </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <cosh /> <ci> b </ci> </apply> <apply> <sinh /> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18