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StruveL






Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveL[nu,z] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/03.10.20.0012.01









  


  










Input Form





D[StruveL[\[Nu], z], {z, \[Alpha]}] == Sum[((-1)^\[Nu] 2^(-1 - 2 k - \[Nu]) z^(1 + 2 k - \[Alpha] + \[Nu]) (Log[z] + PolyGamma[-1 - 2 k - \[Nu]] - PolyGamma[2 + 2 k - \[Alpha] + \[Nu]]))/((-2 - 2 k - \[Nu])! Gamma[3/2 + k] Gamma[3/2 + k + \[Nu]] Gamma[2 + 2 k - \[Alpha] + \[Nu]]), {k, 0, -Floor[(\[Nu] + 3)/2]}] + (2^(\[Alpha] - 2 (1 + \[Nu]) + 4 Floor[(1 + \[Nu])/2]) Sqrt[Pi] z^(1 - \[Alpha] + \[Nu] - 2 Floor[(1 + \[Nu])/2]) Gamma[2 + \[Nu] - 2 Floor[(1 + \[Nu])/2]] HypergeometricPFQRegularized[ {1, (1/2) (2 + \[Nu] - 2 Floor[(1 + \[Nu])/2]), (1/2) (3 + \[Nu] - 2 Floor[(1 + \[Nu])/2])}, {3/2 - Floor[(1 + \[Nu])/2], (1/2) (2 - \[Alpha] + \[Nu] - 2 Floor[(1 + \[Nu])/2]), (1/2) (3 - \[Alpha] + \[Nu] - 2 Floor[(1 + \[Nu])/2]), 3/2 + \[Nu] - Floor[(1 + \[Nu])/2]}, z^2/4])/(-1)^Floor[(1 + \[Nu])/2] /; Element[-\[Nu], Integers] && -\[Nu] > 0










Standard Form





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MathML Form







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</ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQRegularized </ci> <list> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </list> <list> <apply> <plus /> <cn type='rational'> 3 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> &#957; 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</ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; 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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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