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SinhIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > SinhIntegral[z] > Integration > Indefinite integration > Involving direct function and Gamma-, Beta-, Erf-type functions > Involving exponential integral-type functions and a power function > Involving Si and power





http://functions.wolfram.com/06.39.21.0070.01









  


  










Input Form





Integrate[z^2 SinIntegral[b z] SinhIntegral[a z], z] == (1/6) ((1/b^3) (ExpIntegralEi[(a - I b) z] - ExpIntegralEi[(-(a + I b)) z] + ExpIntegralEi[(a + I b) z] - ExpIntegralEi[(-a) z + I b z]) + (1/(2 b^2)) (-((2 E^((a - I b) z))/(I a + b)) + (2 I)/(E^((a + I b) z) (a + I b)) + (2 E^((a + I b) z))/(I a - b) + (2 E^((-a) z + I b z))/(I a + b) + (b Gamma[2, (a - I b) z])/ (I a + b)^2 - (b Gamma[2, (-(a + I b)) z])/((-I) a + b)^2 + (b Gamma[2, (a + I b) z])/((-I) a + b)^2 - (b Gamma[2, (-a) z + I b z])/ (I a + b)^2) - (1/b^3) ((Gamma[3, (-I) b z] + Gamma[3, I b z]) SinhIntegral[a z]) + 2 z^3 SinhIntegral[a z] SinIntegral[b z] + (1/(2 a^3)) (I ((a E^((a - I b) z) (2 I b + a^2 z + a (-3 - I b z)))/ (a - I b)^2 + (a E^((-a) z + I b z) (-2 I b + a^2 z + a (3 - I b z)))/ (a - I b)^2 - (a E^((a + I b) z) (-2 I b + a^2 z + a (-3 + I b z)))/ (a + I b)^2 - (a (2 I b + a^2 z + a (3 + I b z)))/ (E^((a + I b) z) (a + I b)^2) + 2 ExpIntegralEi[(a - I b) z] + 2 ExpIntegralEi[(-(a + I b)) z] - 2 ExpIntegralEi[(a + I b) z] - 2 ExpIntegralEi[(-a) z + I b z] + 2 I (Gamma[3, (-a) z] + Gamma[3, a z]) SinIntegral[b z])))










Standard Form





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MathML Form







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-1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <imaginaryi /> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <plus /> <apply> <ci> Gamma </ci> <cn type='integer'> 3 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='integer'> 3 </cn> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <ci> z </ci> </apply> <cn type='integer'> 3 </cn> </apply> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <imaginaryi /> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> 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Rule Form





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





2001-10-29





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