A probabilistic version of Mehler's formula

DOI10.11650/TJM.18.2014.3576zbMath1357.33019OpenAlexW2082925928MaRDI QIDQ514691

Mingjin Wang

Publication date: 9 March 2017

Published in: Taiwanese Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.11650/tjm.18.2014.3576

zbMATH Keywords

Lebesgue's dominated convergence theoremAl-Salam-Carlitz polynomialsanalytic continuation theoremMehler's formulaq)\)the distribution \(\mathrm{W}(x

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (1)

A \(q\)-operational equation and the Rogers-Szegő polynomials

Cites Work

• A new probability distribution with applications
• The \(q\)-Bernstein basis as a \(q\)-binomial distribution
• \(q\)-integral representation of the Al-Salam-Carlitz polynomials
• On the Gaussian \(q\)-distribution
• More on the umbral calculus, with emphasis on the \(q\)-umbral calculus
• Some multilinear generating functions for q-Hermite polynomials
• A probabilistic proof of the Andrews--Gordon identities
• Some operator identities and \(q\)-series transformation formulas
• PROBABILISTIC DERIVATION OF A q-POLYNOMIALS TRANSFORMATION FORMULA
• A PROBABILISTIC PROOF OF THE ROGERS–RAMANUJAN IDENTITIES
• Unnamed Item

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