Two-parameter Srivastava polynomials and several series identities

Advances in Difference Equations

Mehmet Ali zarslan¹  Cem Kaanoglu² 

[1] Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Gazimagusa, Turkey;Faculty of Engineering, Cyprus International University, Nicosia, Turkey

关键词: Complex Number;    Suitable Choice;    Jacobi Polynomial;    Laguerre Polynomial;    Double Sequence;   

DOI  :  10.1186/1687-1847-2013-81

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In the present paper, we introduce two-parameter Srivastava polynomials in one, two and three variables by inserting new indices, where in the special cases they reduce to (among others) Laguerre, Jacobi, Bessel and Lagrange polynomials. These polynomials include the family of polynomials which were introduced and/or investigated in (Srivastava in Indian J. Math. 14:1-6, 1972; González et al. in Math. Comput. Model. 34:133-175, 2001; Altın et al. in Integral Transforms Spec. Funct. 17(5):315-320, 2006; Srivastava et al. in Integral Transforms Spec. Funct. 21(12):885-896, 2010; Kaanoglu and Özarslan in Math. Comput. Model. 54:625-631, 2011). We prove several two-sided linear generating relations and obtain various series identities for these polynomials. Furthermore, we exhibit some illustrative consequences of the main results for some well-known special polynomials which are contained by the two-parameter Srivastava polynomials. MSC:33C45.

【 授权许可】

CC BY