## 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.

### MSC:

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

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