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StruveH






Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveH[nu,z] > Identities > Recurrence identities > Distant neighbors > Decreasing





http://functions.wolfram.com/03.09.17.0017.01









  


  










Input Form





StruveH[\[Nu], z] == (2^(-1 + n) Pochhammer[1 - \[Nu], -1 + n] (z HypergeometricPFQ[{1, (1 - n)/2, 1 - n/2}, {1, 1 - n, 1 - \[Nu], 1 - n + \[Nu]}, -z^2] StruveH[\[Nu] - n - 1, z] + 2 (n - \[Nu]) HypergeometricPFQ[{1, (1 - n)/2, -(n/2)}, {1, -n, 1 - \[Nu], -n + \[Nu]}, -z^2] StruveH[\[Nu] - n, z]))/ (-z)^n + ((2^(1 - \[Nu]) z^(-1 + \[Nu]))/Sqrt[Pi]) Sum[((4^j Pochhammer[1 - \[Nu], j])/((-z^2)^j Gamma[1/2 - j + \[Nu]])) HypergeometricPFQ[{1, (1 - j)/2, -(j/2)}, {1, -j, 1 - \[Nu], -j + \[Nu]}, -z^2], {j, 0, -1 + n}] /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> StruveH </ci> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 4 </cn> <ci> j </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <ci> j </ci> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#957; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> j </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> <list> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <apply> <plus /> <ci> &#957; 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Rule Form





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Contributed by





Brychkov Yu.A. (2005)










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





2007-05-02





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