# Unified Bernoulli-Euler polynomials of Apostol type

@inproceedings{Belbachir2021UnifiedBP, title={Unified Bernoulli-Euler polynomials of Apostol type}, author={Hac{\`e}ne Belbachir and Yahia Djemmada and S. Hadj-Brahim}, year={2021} }

Abstract The object of this paper is to introduce and study properties of unified Apostol-Bernoulli and Apostol-Euler polynomials noted by {Vn(x; λ;μ)}n≥0. We study some arithmetic properties of {Vn(x; λ;μ)}n≥0 as their connection to Apostol-Euler polynomials and Apostol-Bernoulli polynomials. Also, we give derivation and integration representations of {Vn(x; λ;μ)}n≥0. Finally, we use the umbral calculus approach to deduce symmetric identities.

## References

SHOWING 1-10 OF 12 REFERENCES

Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials

- Mathematics
- 2005

Abstract The main object of this paper is to give analogous definitions of Apostol type (see [T.M. Apostol, On the Lerch Zeta function, Pacific J. Math. 1 (1951) 161–167] and [H.M. Srivastava, Some…

Some Explicit Formulas for Euler-Genocchi Polynomials

- Mathematics, Computer ScienceIntegers
- 2019

The EulerGenocchi family of polynomials introduced recently via its generating function is studied and some combinatorial properties and expressions in terms of alternate power sums and related sums for the Stirling numbers of the second kind are given.

Some Generalizations and Basic (or q-) Extensions of the Bernoulli, Euler

- Mathematics
- 2011

In the vast literature in Analytic Number Theory, one can find systematic and extensive investigations not only of the classical Bernoulli, Euler and Genocchi polynomials and their corresponding…

On the generalization of the Euler polynomials with the real parameters

- Mathematics, Computer ScienceAppl. Math. Comput.
- 2011

The multiple alternating sums with positive real parameters a and b are evaluated in terms of both generalized Euler and generalized Bernoulli polynomials of order α and some interesting special cases are obtained.

On another approach for a family of Appell polynomials

- Mathematics
- 2018

The present study is devoted to some new formulas for a family of Appell polynomials. These formulas are expressed in terms of Bernoulli-Euler and Bernoulli-Genocchi polynomials. Moreover, other…

Applications of the classical umbral calculus

- Mathematics
- 2001

Abstract.We describe applications of the classical umbral calculus to bilinear generating
functions for polynomial sequences, identities for Bernoulli and related numbers, and
Kummer congruences.

Sul calcolo umbrale

- Ricerche di Matematica
- 1994