Lucas-Euler Relations Using Balancing and Lucas-Balancing Polynomials
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions. From these polynomial relations, we deduce interesting identities with Fibonacci and Lucas numbers, and Euler numbers. The results must be regarded as companion results to some Fibonacci-Bernoulli identities, which we derived in our previous paper
Abstract
We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions. From these polynomial relations, we deduce interesting identities with Fibonacci and Lucas numbers, and Euler numbers. The results must be regarded as companion results to some Fibonacci-Bernoulli identities, which we derived in our previous paper
참고문헌 (21)
- P. F. Byrd, "Relations between Euler and Lucas numbers", Fibonacci Quart, 13, pp.111~114 (1975)
- D. Castellanos, "A generalization of Binet’s formula and some of its consequences", Fibonacci Quart, 27(5), pp.424~438 (1989)
- K. Dilcher, "NIST Handbook of Mathematical Functions" (2010), Cambridge University Press
- R. Frontczak, "On balancing polynomials", Appl. Math. Sci, 13, pp.57~66 (2019)
- R. Frontczak, "Relating Fibonacci numbers to Bernoulli numbers via balancing polynomials", J. Integer Seq, 22 (2019)
- ROBERT FRONTCZAK, "ADDITIONAL CLOSE LINKS BETWEEN BALANCING AND LUCAS-BALANCING POLYNOMIALS", Advanced Studies in Contemporary Mathematics, 31(3), pp.287~300 (2021), 장전수학회
- R. Frontczak, "More Fibonacci-Bernoulli relations with and without balancing polynomials", Math. Comm, 26, pp.215~226 (2021)
- R. Frontczak, "Generalized Euler-Genocchi polynomials and Lucas numbers", Integers, 20, pp.A52~ (2020)
- R. P. Kelisky, "On formulas involving both the Bernoulli and Fibonacci numbers", Scripta Math, 23, pp.27~32 (1957)
- D. S. Kim, "On sums of finite products of balancing polynomials", J. Comput. Appl. Math, 377, pp.112913~ (2020)
- 김태균, "A DIFFERENCE OF SUMS OF FINITE PRODUCTS OF LUCAS-BALANCING POLYNOMIALS", Advanced Studies in Contemporary Mathematics, 30(1), pp.121~134 (2020), 장전수학회
- 김태균, "A note on sums of finite products of Lucas-balancing polynomials", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 23(1), pp.1~22 (2020), 장전수학회
- Y. Meng, "A new identity involving balancing polynomials and balancing numbers", Symmetry, 11, pp.1141~ (2019)
- G. Ozdemir, "Identities and relations associated with Lucas and some special sequences", AIP Conf. Proc, 1863, pp.300003~ (2017)
- B. K. Patel, "Incomplete balancing and Lucas-balancing numbers", Math. Reports, 20(1), pp.59~72 (2018)
- P. K. Ray, "Balancing polynomials and their derivatives", Ukrainian Math. J, 69(4), pp.646~663 (2017)
- "The On-Line Encyclopedia of Integer Sequences"[URL]
- T. Wang, "Recurrence sequences and N¨orlund-Euler polynomials", Fibonacci Quart, 34(4), pp.314~319 (1996)
- P. T. Young, "Congruences for Bernoulli-Lucas sums", Fibonacci Quart, 55(5), pp.201~212 (2017)
- Z. Zhang, "Recurrence sequences and Bernoulli polynomials of higher order", Fibonacci Quart, 33(3), pp.359~362 (1995)
- T. Zhang, "On generalized Fibonacci polynomials and Bernoulli numbers", J. Integer Seq, 8 (2005)