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ISSN 1088-6850(e) ISSN 0002-9947(p)

Birth-death processes and -continued fractions

Authors: Tony Feng, Rachel Kirsch, Elise Villella and Matt Wage
Journal: Trans. Amer. Math. Soc. 364 (2012), 2703-2721
MSC (2010): Primary 03B48; Secondary 11A55
Posted: January 17, 2012
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Abstract: In the 1997 paper of Parthasarathy, Lenin, Schoutens, and Van Assche, the authors study a birth-death process related to the Rogers-Ramanujan continued fraction . We generalize their results to establish a correspondence between birth-death processes and a larger family of -continued fractions. It turns out that many of these continued fractions, including , play important roles in number theory, specifically in the theory of modular forms and -series. We draw upon the number-theoretic properties of modular forms to give identities between the transition probabilities of different birth-death processes.

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