Using the Padé approximation of the exponential function, we obtain recurrence relations between Apostol-Bernoulli and between Apostol-Euler polynomials. As applications, we derive some new lacunary recurrence relations for Bernoulli and Euler polynomials with gap of length 4 and lacunary relations for Bernoulli and Euler numbers with gap of length 6.

We apply the theory of disconjugate linear recurrence relations to the study of irrational quantities in number theory. In particular, for an irrational number associated with solutions of three-term linear recurrence relations we show that there exists a four-term linear recurrence relation whose solutions allow us to show that the number is a quadratic irrational if and only if the four-term ...

The aim of this paper is to present some recurrence relations arising from confluent hypergeometric functions. In addition, an explicit closed-form expression for a sequence associated the series in terms Bell partition polynomials proposed. Several examples are given illustrate our results.