Some Formulae of Products of the Apostol-Bernoulli and Apostol-Euler Polynomials
نویسندگان
چکیده
منابع مشابه
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...
متن کاملOn the Multiple Sums of Bernoulli, Euler and Genocchi Polynomials
We introduce and investigate the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials by means of a suitable theirs generating polynomials. We establish several interesting properties of these polynomials. Also, we gave some propositions two theorems and one corollary.
متن کاملFourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials
We investigate Fourier expansions for the Apostol-Bernoulli and Apostol-Euler polynomials using the Lipschitz summation formula and obtain their integral representations. We give some explicit formulas at rational arguments for these polynomials in terms of the Hurwitz zeta function. We also derive the integral representations for the classical Bernoulli and Euler polynomials and related known ...
متن کاملFourier 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.
متن کاملPadé 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.
متن کامل