An Extension Of Generalized Apostol-Euler Polynomials

This paper is for Apostol-Euler polynomial to do further research, It is based on the article (Tremblg in Appl. Math. Let.24(888-1893),2011) which is written by R. Tremblay, S. Gaboury, B.-J. Fugere professors. In the article they introduce a new class of generalized Bernoulli polynomial. Similar to it, the author introduces and investigates an extension of the generalized Apostol-Euler polynomials. She states some properties for these polynomials and obtains some relationships between the polynomials and the Apostol-Bernoulli polynomials, Stirling Numbers of the second kind, Jacobi polynomi-als, Laguerre polynomials, Hermite polynomials and generalized Bernoulli polynomials. And in this article, the author also gets the properties equation which covers the Luo-Srivastave addition.At the end of this article, Appell sequences are joined in, with the definition, it covers Bernoulli polynomial, Euler polynomials and so on. Then with the help of the scries basic theory and the basic equations of the combination, the author get some equations which related to them.