Notes on degenerate numbers

Cenkci M., Howard F. T.

DISCRETE MATHEMATICS, cilt.307, sa.19-20, ss.2359-2375, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 307 Sayı: 19-20
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1016/j.disc.2006.10.013
  • Dergi Adı: DISCRETE MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2359-2375
  • Anahtar Kelimeler: potential and bell polynomials, Bernoulli and Stirling numbers, BERNOULLI NUMBERS, EXPLICIT FORMULAS, BELL POLYNOMIALS, CONGRUENCES
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this pap er, using a theorem relating the potential polynomial F-k((z)) and the exponential Bell polynomial B-n,B-j (0, 0, f(r), f(r+1)....), we obtain some explicit formulas for higher order degenerate Bernoulli numbers of the first and second kinds. We also prove new recurrence formulas for these numbers. Furthermore, we discuss other applications of the theorem, from which we deduce several formulas for degenerate Genocchi numbers, degenerate tangent numbers, and the coefficients of the higher order degenerate Euler polynomials. Finally, we examine the polynomials V (k, j, z I A) and VI (k, 1, z I A), and, in particular, we show how these polynomials are related to the degenerate Bernoulli, Genocchi, tangent, and van der Pol numbers, and the numbers generated by the reciprocal of (1 + lambda x)(1/lambda) - x - 1. (c) 2007 Elsevier B.V. All rights reserved.