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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function and exponential function > Involving products of powers of two direct functions and exponential function > Involving products of powers of two direct functions and exponential function > Involving ep zsinhm(c z) sinhv(a z+b)





http://functions.wolfram.com/01.19.21.2233.01









  


  








Input Form





Integrate[E^(p z) Sinh[c z]^m Sinh[a z + b]^\[Nu], z] == (1/(p + a \[Nu])) ((E^(p z) Binomial[m, m/2] Hypergeometric2F1[ (I (I p + I a \[Nu]))/(2 a), -\[Nu], (1/2) (2 - p/a - \[Nu]), E^(2 I (I b + I a z))] (1 - Mod[m, 2]) Sinh[b + a z]^\[Nu])/ (2^m I^m (1 - E^(2 I (I b + I a z)))^\[Nu])) + (I^(1 - m) Sinh[b + a z]^\[Nu] Sum[(-1)^k Binomial[m, k] ((E^(((-c) (-2 k + m) + p) z) Hypergeometric2F1[ (I (2 I c k - I c m + I p + I a \[Nu]))/(2 a), -\[Nu], (I (2 I c k - I c m + I p + I a (-2 + \[Nu])))/(2 a), E^(2 I (I b + I a z))])/(2 I c k - I c m + I p + I a \[Nu]) + (E^(I m Pi + (c (-2 k + m) + p) z) Hypergeometric2F1[ (I (I c (-2 k + m) + I p + I a \[Nu]))/(2 a), -\[Nu], (I (-2 I c k + I c m + I p + I a (-2 + \[Nu])))/(2 a), E^(2 I (I b + I a z))])/(I c (-2 k + m) + I p + I a \[Nu])), {k, 0, Floor[(1/2) (-1 + m)]}])/(2^m I^m (1 - E^(2 I (I b + I a z)))^ \[Nu]) /; Element[m, Integers] && m > 0








Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <ci> a </ci> <imaginaryi /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <imaginaryi /> <pi /> <ci> m </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <ci> c </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> c </ci> <imaginaryi /> <ci> k </ci> </apply> <apply> <times /> <imaginaryi /> <ci> c </ci> <ci> m </ci> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <ci> a </ci> <imaginaryi /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> c </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> &#957; 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Rule Form





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





2002-12-18