Geodesic
Remodified Bessel functions via coincidences and near coincidences
Journal of integer sequences, Tome 14 (2011) no. 7
By considering a particular probabilistic scenario associated with coincidences, we are led to a family of functions akin to the modified Bessel function of the first kind. These are in turn solutions to a certain family of linear differential equations possessing structural similarities to the modified Bessel differential equation. The Stirling number triangle of the second kind arises quite naturally from these differential equations, as do more complicated, yet related, truncated number triangles, none of which appear in Sloane's On-Line Encyclopedia of Integer Sequences.
Classification : 33C10, 11B73, 33C90, 34A05, 60E05
Keywords: Bessel functions, linear differential equations, Poisson distributions, Stirling numbers of the second kind 
@article{JIS_2011__14_7_a0,
     author = {Griffiths,  Martin},
     title = {Remodified {Bessel} functions via coincidences and near coincidences},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {7},
     zbl = {1217.33007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_7_a0/}
}
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Griffiths,  Martin. Remodified Bessel functions via coincidences and near coincidences. Journal of integer sequences, Tome 14 (2011) no. 7. http://geodesic.mathdoc.fr/item/JIS_2011__14_7_a0/