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Tanh






Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving powers of the direct function and trigonometric functions > Involving powers of cos > Involving cosm(b z)





http://functions.wolfram.com/01.21.21.0280.01









  


  










Input Form





Integrate[Cos[b z]^m Tanh[c z]^\[Nu], z] == ((1/(c (1 + \[Nu]))) Binomial[m, m/2] Tanh[c z]^(1 + \[Nu]) Hypergeometric2F1[(1 + \[Nu])/2, 1, 1 + (1 + \[Nu])/2, Tanh[c z]^2] (1 - Mod[m, 2]))/2^m + ((I (1 + E^(-2 c z))^\[Nu] Tanh[c z]^\[Nu])/ (2^m (1 - E^(-2 c z))^\[Nu] b)) Sum[(1/(m - 2 k)) Binomial[m, k] ((-E^(I b (-2 k + m) z)) AppellF1[-((I b (-2 k + m))/(2 c)), -\[Nu], \[Nu], 1 - (I b (-2 k + m))/(2 c), E^(-2 c z), -E^(-2 c z)] + AppellF1[(I b (-2 k + m))/(2 c), -\[Nu], \[Nu], 1 + (I b (-2 k + m))/(2 c), E^(-2 c z), -E^(-2 c z)]/ E^(I b (-2 k + m) z)), {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> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <tanh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <imaginaryi /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; 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Rule Form





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





2002-12-18