Generalizations of poly-Bernoulli numbers and polynomials

Generalizations of poly-Bernoulli numbers and polynomials

The concepts of poly-Bernoulli numbers [B.sup.(k).sub.n], poly-Bernoulli polynomials and the generalized poly-Bernoulli numbers [B.sup.(k).sub.n] (a, b) are generalized to [B.sup.(k).sub.n] (t, a, b, c) which is called the generalized poly-Bernoulli polynomials depending on real parameters a, b, c....

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Veröffentlicht in:International journal of mathematical combinatorics 2010-07, Vol.2, p.7
Hauptverfasser: Jolany, Hassan, Darafsheh, M R, Alikelaye, R Eizadi
Format: Artikel
Sprache:eng
Schlagworte:
e (Number)
Law of large numbers
Polynomials
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Zusammenfassung:The concepts of poly-Bernoulli numbers [B.sup.(k).sub.n], poly-Bernoulli polynomials and the generalized poly-Bernoulli numbers [B.sup.(k).sub.n] (a, b) are generalized to [B.sup.(k).sub.n] (t, a, b, c) which is called the generalized poly-Bernoulli polynomials depending on real parameters a, b, c. Some properties of these polynomials and some relationships between [B.sup.(k).sub.n](t), [B.sup.(k).sub.n](t), [B.sup.(k).sub.n](a, b) and B(nk)(t, a, b, c) are established. Key Words: Poly-Bernoulli polynomial, Euler number, Euler polynomial. AMS(2000): 11B68, 11B73
ISSN:1937-1055
1937-1047