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Csch






Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and trigonometric functions > Involving powers of cos and powers of cosh > Involving cosm(a z) coshu(b z) csch(c z)





http://functions.wolfram.com/01.23.21.0212.01









  


  










Input Form





Integrate[Cos[a z]^m Cosh[c z]^\[Mu] Csch[c z], z] == ((1/(c (\[Mu] - 1))) 2^(1 - m) Binomial[m, m/2] Cosh[c z]^\[Mu] (1 - Mod[m, 2]) AppellF1[-((\[Mu] - 1)/2), -\[Mu], 1, (3 - \[Mu])/2, -E^(-2 c z), E^(-2 c z)])/(E^(c z) (1 + E^(-2 c z))^\[Mu]) + (2^(1 - m) Cosh[c z]^\[Mu] Sum[((E^(I a (m - 2 s) z) AppellF1[-((I a m - 2 I a s + c \[Mu] - c)/ (2 c)), -\[Mu], 1, -((I a m - 2 I a s + c (-3 + \[Mu]))/(2 c)), -E^(-2 c z), E^(-2 c z)])/(I a (m - 2 s) + c \[Mu] - c) + (E^(((-I) a m + 2 I a s) z) AppellF1[(I a m - 2 I a s - c \[Mu] + c)/ (2 c), -\[Mu], 1, (I a m - 2 I a s + c (3 - \[Mu]))/(2 c), -E^(-2 c z), E^(-2 c z)])/((-I) a m + 2 I a s + c \[Mu] - c)) Binomial[m, s], {s, 0, Floor[(1/2) (-1 + m)]}])/ (E^(c z) (1 + E^(-2 c z))^\[Mu]) /; Element[m, Integers] && m > 0










Standard Form





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MathML Form







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</ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <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> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> </apply> <apply> <power /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> &#956; </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> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> AppellF1 </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> &#956; 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Rule Form





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





2002-12-18





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