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DIMORPHIC MERSENNE NUMBERS AND THEIR APPLICATIONS

김태균|김대산
장전수학회 (Jangjeon Mathematical Society)|2022.10|Advanced Studies in Contemporary Mathematics|제32권 제4호|pp. 435-441

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참고문헌

키워드

degenerate Bernoulli polynomialsdimorphic Mersenne numbersincomplete Bell polynomials
주제분류수학

초록

The Mersenne primes are primes which can be written as some prime power of 2 minus 1. These primes were studied from antiquity in that their close connection with perfect numbers and even to present day in that their easiness for primality test. In this paper, we introduce the dimorphic Mersenne numbers as a degenerate version of the Mersenne numbers and investigate some of their properties in connection with the degenerate Bernoulli polynomials and the incomplete Bell polynomials.

Abstract

The Mersenne primes are primes which can be written as some prime power of 2 minus 1. These primes were studied from antiquity in that their close connection with perfect numbers and even to present day in that their easiness for primality test. In this paper, we introduce the dimorphic Mersenne numbers as a degenerate version of the Mersenne numbers and investigate some of their properties in connection with the degenerate Bernoulli polynomials and the incomplete Bell polynomials.

참고문헌 (19)

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  2. Burton, D. M., "Elementary number theory", pp.xviii+450~ (1989), W. C. Brown Publishers
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  8. Kim, D. S., "A note on a new type of degenerate Bernoulli numbers", Russ. J. Math. Phys, 27(2), pp.227~235 (2020)
  9. Kim, D. S., "Degenerate Sheffer sequences and λ-Sheffer sequences", J. Math. Anal. Appl, 493(1), pp.124521~ (2021)
  10. Kim, D. S., "Some new formulas of complete and incomplete degenerate Bell polynomials", Adv. Difference Equ, pp.10~ (2021)
  11. 김혜경, "INCOMPLETE AND COMPLETE r-CENTRAL LAH-BELL POLYNOMIALS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 25(1), pp.95~111 (2022), 장전수학회
  12. 김택연, "DEGENERATE COMPLETE BELL POLYNOMIALS AND NUMBERS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(4), pp.533~543 (2017), 장전수학회[DOI]
  13. Kim, T., "On some degenerate differential and degenerate difference operators", Russ. J. Math. Phys, 29(1), pp.37~46 (2022)
  14. Kim, T., "Degenerate Laplace transform and degenerate gamma function", Russ. J. Math. Phys, 24(2), pp.241~248 (2017)
  15. Kim, T., "Complete and incomplete Bell polynomials associated with Lah-Bell numbers and polynomials", Adv. Difference Equ, pp.12~ (2021)
  16. Taekyun Kim, "SOME IDENTITIES INVOLVING DEGENERATE r-STIRLING NUMBERS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 25(2), pp.245~252 (2022), 장전수학회
  17. Kwon, J., "Some identities for degenerate complete and incomplete r-Bell polynomials", J. Inequal. Appl, pp.9~ (2020)
  18. 마민영, "SOME IDENTITIES ON THE FULLY DEGENERATE BELL POLYNOMIALS OF THE SECOND KIND", Advanced Studies in Contemporary Mathematics, 30(1), pp.145~154 (2020), 장전수학회
  19. YILMAZ SIMSEK, "CONSTRUCTION OF GENERALIZED LEIBNITZ TYPE NUMBERS AND THEIR PROPERTIES", Advanced Studies in Contemporary Mathematics, 31(3), pp.311~323 (2021), 장전수학회

관련 논문AI추천

SOME PROPERTIES OF GENERALIZED DEGENERATE BERNOULLI POLYNOMIALS AND NUMBERS권종겸, 김원주, Lee-Chae Jang장전수학회 · Advanced Studies in Contemporary Mathematics2022 · 제32권 제4호Some identities of the type 2 degenerate Bernoulli and Euler numbers권종겸, 김대산, 장관우, 정세교장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제4호DEGENERATE POLYEXPONENTIAL FUNCTIONS AND POLY-EULER POLYNOMIALSBURAK KURT대한수학회 · 대한수학회논문집2021 · 제36권 제1호A note on type 2 degenerate multi-poly-Bernoulli polynomials of the second kindM. KAMARUJJAMA, Waseem A. Khan장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2022 · 제25권 제1호ON THE DEGENERATE CAUCHY NUMBERS AND POLYNOMIALS김태균장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제3호A NOTE ON THE MODIFIED TYPE 2 DEGENERATE POLY-CHANGHEE-GENOCCHI NUMBERS AND POLYNOMIALS김한영, 장이채장전수학회 · Advanced Studies in Contemporary Mathematics2021 · 제31권 제3호

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