Apostol Bernoulli-Fibonacci Polynomials, Apostol Euler-Fibonacci Polynomials and Their Generating Functions

Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials

We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials Bn(x;λ) in detail. The starting point is their Fourier series on [0, 1] which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane. This is used to determine explicit estimates on the constants in the approximation, and also to analyze oscillatory phenomena which arise in certain ...

Some results on the Apostol-Bernoulli and Apostol-Euler polynomials

The main object of this paper is to investigate the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials. We first establish two relationships between the generalized Apostol-Bernoulli and Apostol-Euler polynomials. It can be found that many results obtained before are special cases of these two relationships. Moreover, we have a study on the sums of products of the Apostol-Bernoulli...

Fourier expansions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials

We find Fourier expansions of Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. We give a very simple proof of them.

Some Formulae of Products of the Apostol-Bernoulli and Apostol-Euler Polynomials

Padé Approximation and Apostol-Bernoulli and -Euler Polynomials

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.