Continued fraction representation of the generating function of Bernoulli polynomials

Abstract

Continued fraction and quasi-reciprocal continued fraction expansions of the generating function of Bernoulli numbers have been obtained. The convergence and uniform convergence of continued fraction expansions have been proved. Representations of the generating function of Bernoulli polynomials in the form of the product of three continued fractions, as well as the product of three quasi-reciprocal continued fractions, have been found.