On Generalized Lagrange-Based Apostol-type and Related Polynomials
Download PDF
Authors: W. A. KHAN
DOI: 10.46793/KgJMat2206.865K
Abstract:
In this article, we introduce a new class of generalized polynomials, ascribed to the new families of generating functions and identities concerning Lagrange, Hermite, Miller-Lee, and Laguerre polynomials and of their associated forms. It is shown that the proposed method allows the derivation of sum rules involving products of generalized polynomials and addition theorems. We develop a point of view based on generating relations, exploited in the past, to study some aspects of the theory of special functions. The possibility of extending the results to include generating functions involving products of Lagrange-based unified Apostol-type and other polynomials is finally analyzed.
Keywords:
Lagrange polynomials, Lagrange-Hermite polynomials, Lagrange-based unified Apostol type polynomials, Miller-Lee polynomials, Laguerre polynomials.
References:
[1] A. Altin and E. Erkus, On a multivariable extension of the Lagrange-Hermite polynomials, Integral Transforms Spec. Funct. 17 (2006), 239–244.
[2] W. Ch. C. Chan, Ch. J. Chyan and H. M. Srivastava, The Lagrange polynomials in several variables, Integral Transforms Spec. Funct. 12(2) (2001), 139–148.
[3] G. Dattoil, P. E. Ricci and C. Cesarano, The Lagrange polynomials the associated generalizations, and the umbral calculus, Integral Transforms Spec. Funct. 14 (2003), 181–186.
[4] G. Dattoli, S. Lorenzutta and D. Sacchetti, Integral representations of new families of polynomials, Italian Journal of Pure and Applied Mathematics 15 (2004), 19–28.
[5] E. Erkus and H. M. Srivastava, A unified presentation of some families of multivariable polynomials, Integral Transforms Spec. Funct. 17 (2006), 267–273.
[6] W. A. Khan, Some properties of Hermite-based Apostol-type polynomials, Kyungpook Math. J. 55 (2015), 597–614.
[7] W. A. Khan and H. Haroon, Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials, Springer Plus 5 (2016), Article ID 1920.
[8] W. A. Khan and M. A. Pathan, On generalized Lagrange Hermite-Bernoulli and related polynomials, Acta Comm. Univ. Tart. Math. 23(2) (2019), 211–224.
[9] V. Kurt, Some symmetry identities for the Apostol-type polynomials related to multiple alternating sums, Adv. Difference Equ. 2013(1) (2013), Article ID 32.
[10] V. Kurt, Some symmetry identities for the unified Apostol-type polynomials and multiple power sums, Filomat 30(3) (2016), 583–592.
[11] Q. M. Luo and H. M. Srivastava, Some series identities involving the Apostol-type and related polynomials, Comp. Math. Appl. 62 (2011), 3591–3602.
[12] Q. M. Luo, The multiplication formulas for the Apostol-Bernoulli and Apostol-Euler polynomials of higher order, Integral Trans. Spec. Func. 20 (2009), 377–391.
[13] Q. M. Luo, The multiplication formulas for Apostol-type polynomials and multiple alternating sums, Math. Notes 91 (2012), 46–57.
[14] M. A. Ozarslan, Unified Apostol-Bernoulli, Euler and Genocchi polynomials, Comp. Math. Appl. 62 (2011), 2482–2462.
[15] H. Ozden, Y. Simsek and H. M. Srivastava, A unified presentation of the generating function of the generalized Bernoulli, Euler and Genocchi polynomials, Comp. Math. Appl. 60 (2010), 2779–2789.
[16] H. Ozden and Y. Simsek, Modification and unification of the Apostol-type numbers and polynomials, Appl. Math. Comp. 235 (2014), 338–351.
[17] M. A. Pathan and W. A. Khan, Some implicit summation formulas and symmetric identities for the generalized Hermite-based polynomials, Acta Univ. Apulensis Math. Inform. 13 (2014), 113–136.
[18] M. A. Pathan and W. A. Khan, Some implicit summation formulas and symmetric identities for the generalized Hermite-Bernoulli polynomials, Mediterr. J. Math. 12 (2015), 679–695.
[19] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, John Wiley and Sons, New York, Chichester, Brisbane, Toronto, 1984.
Login:
