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http://functions.wolfram.com/01.20.21.4795.01
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Integrate[Cos[d z] (a Sinh[e z] + b Cosh[e z])^\[Beta], z] ==
(1/2) (-((1/(I d + e \[Beta]))
((((a (-1 + E^(2 e z)) + b (1 + E^(2 e z)))/E^(e z))^\[Beta]
Hypergeometric2F1[((-I) d - e \[Beta])/(2 e), -\[Beta],
(1/2) (2 - (I d)/e - \[Beta]), ((a + b) E^(2 e z))/(a - b)])/
(2^\[Beta] E^(I d z) (1 + ((a + b) E^(2 e z))/(-a + b))^\[Beta]))) -
(1/((-I) d + e \[Beta]))
((E^(I d z) ((a (-1 + E^(2 e z)) + b (1 + E^(2 e z)))/E^(e z))^\[Beta]
Hypergeometric2F1[(I d - e \[Beta])/(2 e), -\[Beta],
(1/2) (2 + (I d)/e - \[Beta]), ((a + b) E^(2 e z))/(a - b)])/
(2^\[Beta] (1 + ((a + b) E^(2 e z))/(-a + b))^\[Beta])))
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/> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> d </ci> </apply> <apply> <times /> <ci> e </ci> <ci> β </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> β </ci> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> β </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> e </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <ci> β </ci> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> e </ci> <ci> β </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> β </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <imaginaryi /> <ci> d </ci> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> β </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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