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Generalized higher order Bernoulli number pairs and generalized Stirling number pairs. (English) Zbl 1221.11061
Given a formal power series f(t)= k=1 f k t k k! and its compositional inverse g(t)= k=1 g k t k k!, the higher order Bernoulli numbers of the first and second kind associated with the series f(t) are defined, some explicit expressions and recurrence relations are given, and plenty of relations including Stirling numbers are derived.
MSC:
11B68Bernoulli and Euler numbers and polynomials
11B73Bell and Stirling numbers
05A19Combinatorial identities, bijective combinatorics
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