TRIPLE SYMMETRIC IDENTITIES FOR w-CATALAN POLYNOMIALS
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we introduce $w$-Catalan polynomials as a generalization of Catalan polynomials and derive fourteen basic identities of symmetry in three variables related to $w$-Catalan polynomials and analogues of alternating power sums. In addition, specializations of one of the variables as one give us new and interesting identities of symmetry even for two variables. The derivations of identities are based on the $p$-adic integral expression for the generating function of the $w$-Catalan polynomials and the quotient of $p$-adic integrals for that of the analogues of the alternating power sums.
Abstract
In this paper, we introduce $w$-Catalan polynomials as a generalization of Catalan polynomials and derive fourteen basic identities of symmetry in three variables related to $w$-Catalan polynomials and analogues of alternating power sums. In addition, specializations of one of the variables as one give us new and interesting identities of symmetry even for two variables. The derivations of identities are based on the $p$-adic integral expression for the generating function of the $w$-Catalan polynomials and the quotient of $p$-adic integrals for that of the analogues of the alternating power sums.
참고문헌 (16)
- F. Ardila, "Catalan Numbers", Math. Inteligencer, 38(2), pp.4~5 (2016)
- U. Duran, "SYMMETRIC IDENTITIES INVOLVING WEIGHTED q-GENOCCHI POLYNOMIALS UNDER S4", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 18(4), pp.455~465 (2015), 장전수학회
- Y. He, "Symmetric identities for Carlitz’s q-Bernoulli numbers and polynomials", Adv. Difference Equ, 2013(246), pp.10~ (2013)
- Y. He, "New symmetric identities involving the Eulerian polynomials", J. Comput. Anal. Appl, 17(3), pp.498~504 (2014)
- K. Inkeri, "On Catalan’s problem", Acta Arith, 9, pp.285~290 (1964)
- 김대산, "Identities associated with generalized twisted Euler polynomials twisted by ramified roots of unity", Advanced Studies in Contemporary Mathematics, 22(3), pp.363~377 (2012), 장전수학회
- 김대산, "Abundant symmetry for higher-order Bernoulli polynomials (I)", Advanced Studies in Contemporary Mathematics, 23(3), pp.459~479 (2013), 장전수학회
- 김대산, "Identities of symmetry for higher-order Euler polynomials in three variables (I)", Advanced Studies in Contemporary Mathematics, 22(1), pp.51~74 (2012), 장전수학회
- T. Kim, "Symmetry p-adic invariant integral on Zp for Bernoulli and Euler polynomials", J. Difference Equ. Appl, 14(12), pp.1267~1277 (2008)
- T. Kim, "Symmetry of power sum polynomials and multivariate fermionic p-adic invari-ant integral on Zp", Russ. J. Math. Phys, 16(1), pp.93~96 (2009)
- T. Kim, "An identity of symmetry for the generalized Euler polynomials", J. Comput. Anal. Appl, 13(7), pp.1292~1296 (2011)
- T. Kim, "A new approach to Catalan numbers using differential equations", arXiv:1605.05927, ~
- T. Kim, "Symmetric identities for an analogue of Catalan polynomials", ~
- A. Natucci, "Recerche sistematiche intorno al “teorema di Catalan”", (Italian) Giorn. Mat. Battaglini (5), 2(82), pp.297~300 (1954)
- 1984, , pp.Pure and Applied Mathematics, 111, ~
- A. Rotkiewicz, "Sur le problem de Catalan", (French) Elem. Math, 15, pp.121~124 (1960)