NEW CLASSES OF RECURRENCE RELATIONS INVOLVING HYPERBOLIC FUNCTIONS, SPECIAL NUMBERS AND POLYNOMIALS

Applicable Analysis and Discrete Mathematics

article

Yilmaz Simsek¹ 

[1] Department of Mathematics, Faculty of Science University of Akdeniz TR-07058 Antalya

关键词: Special functions and polynomials;    Finite differences methods;    Bernoulli and Euler numbers;    recurrence relations;    generating functions;   

DOI  :  10.2298/AADM201020015S

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

By using the calculus of finite differences methods and the umbral calculus,we construct recurrence relations for a new class of special numbers. Usingthis recurrence relation, we define generating functions for this class of specialnumbers and also new classes of special polynomials. We investigate someproperties of these generating functions. By using these generating functionswith their functional equations, we obtain many new and interesting identitiesand relations related to these classes of special numbers and polynomials, theBernoulli numbers and polynomials, the Euler numbers and polynomials, theStirling numbers. Finally, some derivative formulas and integral formulas forthese classes of special numbers and polynomials are given. In general, thisarticle includes results that have the potential to be used in areas such asdiscrete mathematics, combinatorics analysis and their applications.

【 授权许可】

Unknown