Journal of Integer Sequences, Vol. 14 (2011), Article 11.7.1

Remodified Bessel Functions via Coincidences and Near Coincidences

Martin Griffiths
School of Education
University of Manchester
M13 9PL
United Kingdom


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.

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(Concerned with sequences A000127 A001296 A001297 A001298 A008277.)

Received January 28 2011; revised version received May 29 2011. Published in Journal of Integer Sequences, June 11 2011.

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