| Summary: | In this paper, we investigate some identities on Bernoulli numbers and polynomials and those on degenerate Bernoulli numbers and polynomials arising from certain <i>p</i>-adic invariant integrals on <inline-formula> <math display="inline"> <semantics> <msub> <mi mathvariant="double-struck">Z</mi> <mi>p</mi> </msub> </semantics> </math> </inline-formula>. In particular, we derive various expressions for the polynomials associated with integer power sums, called integer power sum polynomials and also for their degenerate versions. Further, we compute the expectations of an infinite family of random variables which involve the degenerate Stirling polynomials of the second and some value of higher-order Bernoulli polynomials.
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