Abstract
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.
Highlights
Let {An,k}∞ n,k= be a bounded double sequence of real or complex numbers, let [a] denote the greatest integer in a ∈ R, and let (λ)ν, (λ) ≡, denote the Pochhammer symbol defined by (λ + ν) (λ)ν := (λ) by means of familiar gamma functions
Where N is the set of positive integers
In this paper we introduce the two-parameter Srivastava polynomials in one and more variables by inserting new indices
Summary
Let {An,k}∞ n,k= be a bounded double sequence of real or complex numbers, let [a] denote the greatest integer in a ∈ R, and let (λ)ν , (λ) ≡ , denote the Pochhammer symbol defined by (λ + ν) (λ)ν := (λ) by means of familiar gamma functions. In , Srivastava [ ] introduced the following family of polynomials: SnN (z) := In [ ], the following family of bivariate polynomials was introduced: Snm,N (x, y) In [ ], Srivastava et al introduced the three-variable polynomials
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