On a \(q\)-analogue of the \(p\)-adic log gamma functions and related integrals. (English) Zbl 0941.11048

The author proposes a definition of a \(q\)-analogue of the \(p\)-adic Haar distribution. The resulting Volkenborn-type integral leads, in particular, to an integral representation of \(q\)-Bernoulli numbers. In turn, the latter is used for obtaining new identities for \(q\)-Bernoulli numbers, \(q\)-Bernoulli polynomials, and for a \(q\)-analogue of the Diamond log gamma function.


11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
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