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BesselI






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselI[nu,z] > Representations through more general functions > Through Meijer G > Classical cases involving Bessel K





http://functions.wolfram.com/03.02.26.0088.01









  


  










Input Form





BesselI[\[Nu], Sqrt[z]] BesselK[-1 - n - \[Nu], Sqrt[z]] == (((-1)^n Pi^(3/2) Csc[(1/4) Pi ((-1)^n + 4 \[Nu])])/Sqrt[2]) MeijerG[{{0, 1/2}, {3/4 + \[Nu], 1/4}}, {{(1 + n)/2, (1 + n)/2 + \[Nu]}, {3/4 + \[Nu], 1/4, -((1 + n)/2), -((1 + n)/2) - \[Nu]}}, z] - (-1)^n Sqrt[Pi] Csc[\[Nu] Pi] Sum[(((-1)^Floor[(1 + n)/2] z^((-1 + 2 k - n)/2) Gamma[1/2 + k - n + Floor[n/2]])/(k! Gamma[k - n - \[Nu]] Gamma[1 + k + \[Nu]])) Pochhammer[1 - k + Floor[n/2], n - Floor[n/2]], {k, 0, Floor[n/2]}] /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> k </ci> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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