# Double Sum involving Product of Appell-Type Bernoulli and Euler Polynomials

## TL;DR

This paper derives a bilateral generating function involving the product of Appell-type Bernoulli and Euler polynomials, expressed through the Hurwitz zeta function, with special cases and integral formulas.

## Contribution

It introduces a new bilateral generating function for Appell-type Bernoulli and Euler polynomials and connects it to the Hurwitz zeta function.

## Key findings

- Derived a bilateral generating function involving Bernoulli and Euler polynomials.
- Expressed the generating function in terms of the Hurwitz zeta function.
- Provided special cases and integral formulas related to the generating function.

## Abstract

In this work we derive a bilateral generating function involving the product of an Appell-type product of the Bernoulli and Euler polynomials over independent indices and orders. This function is expressed in terms of the Hurwitz zeta function and special cases in terms of the finite sum of the Hurwitz zeta function and integral formula are derived.