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Zbl 1092.11045
Kim, T.
$q$-Volkenborn integration. (English)
[J] Russ. J. Math. Phys. 9, No. 3, 288-299 (2002). ISSN 1061-9208; ISSN 1555-6638/e

Summary: The ``complete sum for $q$-Bernoulli polynomials'' is evaluated by using the $q$-Volkenborn integral. This sum helps us to treat the relationships between $q$-Volkenborn integral and non-Archimedean combinatorial analysis. Also $q$-analogs of Stirling number identities are formulated, and the interconsistency among the $q$-analogs of the Stirling numbers and of the Bernoulli numbers is investigated; $p$-adic valued $q$-Bernoulli distributions and related probability properties of Bernoulli measures are studied in connection with a stochastic biological model.

MSC 2000:: *11S80 Other analytic theory of local fields
11B68 Bernoulli numbers, etc.
33D15 Basic hypergeometric functions of one variable

Cited in: Zbl 1238.11022 Zbl 1225.11025 Zbl 1205.11023 Zbl 1179.11007 Zbl 1160.11013 Zbl 1228.11172 Zbl 1148.11011 Zbl 1098.11017 Zbl 1093.11072

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