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SinIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > SinIntegral[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving logarithm and a power function > Involving log and power





http://functions.wolfram.com/06.37.21.0046.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) Log[b z] SinIntegral[a z], z] == (1/(2 \[Alpha]^3)) ((z^\[Alpha] (I (a^2 z^2)^\[Alpha] HypergeometricPFQ[{\[Alpha], \[Alpha]}, {1 + \[Alpha], 1 + \[Alpha]}, (-I) a z] - I (a^2 z^2)^\[Alpha] HypergeometricPFQ[{\[Alpha], \[Alpha]}, {1 + \[Alpha], 1 + \[Alpha]}, I a z] + \[Alpha] ((-I) ((((-I) a z)^\[Alpha] - (I a z)^\[Alpha]) Gamma[1 + \[Alpha]] Log[z] + (I a z)^\[Alpha] Gamma[\[Alpha], (-I) a z] (-1 + \[Alpha] Log[b z]) - ((-I) a z)^\[Alpha] Gamma[\[Alpha], I a z] (-1 + \[Alpha] Log[b z])) + 2 (a^2 z^2)^\[Alpha] (-1 + \[Alpha] Log[b z]) SinIntegral[a z])))/ (a^2 z^2)^\[Alpha])










Standard Form





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MathML Form







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</ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> <ci> &#945; </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#945; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> <ci> &#945; </ci> </apply> <apply> <ci> Gamma </ci> <ci> &#945; </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> &#945; </ci> <apply> <ln /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





© 1998-2014 Wolfram Research, Inc.