Some Identities On Generalized Apostol-Bernoulli-Euler Polynomials And Their Q-Anologue

In this theis, we mainly research Bernoulli number, Euler number, Bernoulli polyno-mials, Euler polynomials, meanwhile we also discuss q-Apostol-Bernoulli polynomials andq-Apostol-Euler polynomials. And we obtain some new identities about them.In the first chapter, we introduce basic definitions and some notations about Bernoullipolynomial and Euler polynomial.In the second chapter, several symmetric identities are given on the generalized Apostol-Euler polynomials by applying the generating functions. Meanwhile, we obtain somenew identities about the generalized Apostol-Bernoulli polynomials and the generalizedApostol-Euler polynomials.In the third chapter, we focus on reseraching q-Apostol-Bernoulli polynomials, q-Apostol-Euler polynomials and obtain some new identities.