Journal article

Generalizing the Reciprocal Logarithm Numbers by Adapting the Partition Method for a Power Series Expansion

Victor Kowalenko

ACTA APPLICANDAE MATHEMATICAE | SPRINGER | Published : 2009

Abstract

Recently, a novel method based on the coding of partitions was used to determine a power series expansion for the reciprocal of the logarithmic function, viz. z/ln∈(1+z). Here we explain how this method can be adapted to obtain power series expansions for other intractable functions. First, the method is adapted to evaluate the Bernoulli numbers and polynomials. As a result, new integral representations and properties are determined for the former. Then via another adaptation of the method we derive a power series expansion for the function z s /ln∈ s (1+z), whose polynomial coefficients A k (s) are referred to as the generalized reciprocal logarithm numbers because they reduce to the recipr..

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University of Melbourne Researchers