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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.
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참고문헌 (16)
참고문헌 신청
F. Ardila / 2016 / Catalan Numbers / Math. Inteligencer 38(2):4~5
U. Duran / 2015 / SYMMETRIC IDENTITIES INVOLVING WEIGHTED q-GENOCCHI POLYNOMIALS UNDER S4 / Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) 18(4):455~465
Y. He / 2013 / Symmetric identities for Carlitz’s q-Bernoulli numbers and polynomials / Adv. Difference Equ 2013(246):10
Y. He / 2014 / New symmetric identities involving the Eulerian polynomials / J. Comput. Anal. Appl 17(3):498~504
K. Inkeri / 1964 / On Catalan’s problem / Acta Arith 9:285~290
U. Duran / 2015 / SYMMETRIC IDENTITIES INVOLVING WEIGHTED q-GENOCCHI POLYNOMIALS UNDER S4 / Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) 18(4):455~465
Y. He / 2013 / Symmetric identities for Carlitz’s q-Bernoulli numbers and polynomials / Adv. Difference Equ 2013(246):10
Y. He / 2014 / New symmetric identities involving the Eulerian polynomials / J. Comput. Anal. Appl 17(3):498~504
K. Inkeri / 1964 / On Catalan’s problem / Acta Arith 9:285~290
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