Şimşek, Yılmaz2022-09-072022-09-072014-05-25Özden, H. ve Şimşek, Y. (2014). "Modification and unification of the Apostol-type numbers and polynomials and their applications". Applied Mathematics and Computation, 235, 338-351.0096-30031873-5649https://doi.org/10.1016/j.amc.2014.03.004https://www.sciencedirect.com/science/article/pii/S0096300314003579http://hdl.handle.net/11452/28531In this paper, we construct generating functions for modification and unification of the Apostol-type polynomials Y ((nu))(n,beta)(x;k,a,b) of order nu. By using these generating functions, we derive many new identities related to the generalized Stirling type numbers of the second kind, array-type polynomials, Eulerian polynomials and the modification and unification of the Apostol-type polynomials and numbers. We give many applications related to these numbers and polynomials and PDEs.eninfo:eu-repo/semantics/closedAccessBernoulli numbers and polynomialsEuler numbers and polynomialsGenocchi Bernoulli numbers and polynomialsStirling numbersCatalan numbersUnified presentationEuler polynomialsGenerating-functionsBernoulliFamiliesMathematicsComputational methodsMathematical techniquesBernoulli numbersEuler numbersEulerian polynomialGenerating functionsSecond kindsStirling numberStirling-typePolynomialsArticle0003358985000352-s2.0-84897431297338351235Mathematics, appliedEuler Polynomials; Bernoulli Numbers; Degenerate