×

zbMATH — the first resource for mathematics

Identities involving Laguerre polynomials derived from umbral calculus. (English) Zbl 1314.33010
Summary: In this paper, we investigate some identities for Laguerre polynomials involving Bernoulli and Euler polynomials derived from umbral calculus.

MSC:
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Carlitz, L, Some generating functions for Laguerre polynomials, Duke Math. J., 35, 825-827, (1968) · Zbl 0167.35202
[2] Dere, R; Simsek, Y, Applications of umbral algebra to some special polynomials, Adv. Stud. Contemp. Math., 22, 433-438, (2012) · Zbl 1270.11018
[3] Dere, R; Simsek, Y, Genocchi polynomials associated with the umbral algebra, Appl. Math. Comput., 218, 756-761, (2011) · Zbl 1229.11036
[4] Ernst, T, Examples of a \(q\)-umbral calculus, Adv. Stud. Contemp. Math., 16, 1-22, (2008) · Zbl 1151.33009
[5] Fang, Q; Wang, T, Umbral calculus and invariant sequences, Ars Combin., 101, 257-264, (2011) · Zbl 1265.05053
[6] D. S. Kim, T. Kim, S. H. Lee, and S. H. Rim, “Frobenius-Euler Polynomials and Umbral Calculus in the \(p\)-Adic Case,” Adv. Difference Equ. 222 (2012). · Zbl 1377.11026
[7] D. S. Kim and T. Kim, “Some Identities of Frobenius-Euler Polynomials Arising from Umbral Calculus,” Adv. Difference Equ. 196 (2012). · Zbl 1377.11025
[8] D. S. Kim, T. Kim, S. H. Lee, and Y. H. Kim, “Some Identities for the Product of Two Bernoulli and Euler Polynomials,” Adv. Difference Equ. 95 (2012). · Zbl 1346.33008
[9] T. Kim, S. H. Rim, D. V. Dolgy, and S. H. Lee, “Some Identities on Bernoulli and Euler Polynomials Arising from the Orthogonality of Laguerre Polynomials,” Adv. Difference Equ. 201 (2012). · Zbl 1377.11028
[10] Kim, T, Some identities on the \(q\)-Euler polynomials of higher order and \(q\)-Stirling numbers by the fermionic \(p\)-adic integral on Z\(p\), Russ. J. Math. Phys., 16, 484-491, (2009) · Zbl 1192.05011
[11] Kwaśniewski, A K, More on the Bernoulli-Taylor formula for extended umbral calculus, Adv. Appl. Clifford Algebras, 16, 29-39, (2006) · Zbl 1119.05013
[12] Roman, S, More on the umbral calculus, with emphasis on the \(q\)-umbral calculus, J. Math. Anal. Appl., 107, 222-254, (1985) · Zbl 0654.05004
[13] S. Roman, The Umbral Calculus (Dover Publ. Inc., New York, 2005). · Zbl 0536.33001
[14] Robinson, T J, Formal calculus and umbral calculus, Formal calculus and umbral calculus, 17, 31, (2010) · Zbl 1226.05050
[15] Ryoo, C, Some relations between twisted q-Euler numbers and Bernstein polynomials, Adv. Stud. Contemp. Math., 21, 217-223, (2011) · Zbl 1266.11040
[16] Simsek, Y, Special functions related to Dedekind-type DC-sums and their applications, Russ. J. Math. Phys., 17, 495-508, (2010) · Zbl 1259.11045
[17] Simsek, Y, Generating functions of the twisted Bernoulli numbers and polynomials associated with their interpolation functions, Adv. Stud. Contemp. Math., 16, 251-278, (2008) · Zbl 1173.11064
[18] Sun, X-H, On umbral calculus, I, J. Math. Anal. Appl., 244, 279-290, (2000) · Zbl 0961.05004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.