Birth-death processes and $q$-continued fractions

DOI10.1090/S0002-9947-2012-05522-XzbMath1271.11007MaRDI QIDQ5390257

Matthew Wage, Tony Feng, Elise Villella, Rachel Kirsch

Publication date: 27 April 2012

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

modular formpositive recurrencebirth-death process\(q\)-continued fractiontransient processrecurrent process

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Continued fractions (11A55) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Continued fractions; complex-analytic aspects (30B70)

Cites Work

• Orthogonal polynomials associated with the Rogers-Ramanujan continued fraction
• Ramanujan's continued fraction
• The ratio of q-like orthogonal polynomials
• The zeros of basic Bessel functions, the functions J(nu+ax)(x), and associated orthogonal polynomials
• Continuous-time Markov chains. An applications-oriented approach
• A birth and death process related to the Rogers-Ramanujan continued fraction
• On the Hellmann-Feynman theorem and the variation of zeros of certain special functions
• A Perron-Frobenius theorem for positive quasipolynomial matrices associated with homogeneous difference equations
• Modular forms and Eisenstein's continued fractions
• The Differential Equations of Birth-and-Death Processes, and the Stieltjes Moment Problem
• The continued fractions found in the unorganized portions of Ramanujan’s notebooks
• Continued fractions and modular functions
• Quantum calculus
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