Bernoulli polynomial

Bernoulli polynomial

[ber‚nü·lē ‚päl·ə′nō·mē·əl]
(mathematics)
The n th such polynomial is where (nk) is a binomial coefficient, and Bk is a Bernoulli number.
References in periodicals archive ?
0] [member of] (0, 1/2) is a unique zero point (in the interval (0,1/2)) of the Bernoulli polynomial [B.
Finally, we specially note that if k is even then the corresponding Bernoulli polynomial [B.
2k](t) the Bernoulli polynomial and {t} = t - [t] the fractional part of t.
Bernoulli polynomials play an important role in various expansions and approximation formulas which are useful both in analytic theory of numbers and in classical and numerical analysis.
In mathematics, the Bernoulli polynomials occur in the study of many special functions and in particular the Riemann zeta function and the Hurwitz zeta function.
In our work we have established certain indefinite integrals involving Fibonacci polynomials, Lucas polynomials, Bernoulli polynomials and Hermite polynomials.
The essential ingredients of the recipe are the Bernoulli polynomials and their relatives.
Terao, The Shi arrangements and the Bernoulli polynomials, Bull.
For some details on the Bernoulli polynomials and the Bernoulli numbers, see for example (8), (9).
Qi in [11] and [13]-[15], defined the generalization of Bernoulli polynomials as
In the usual notation, the n-th Bernoulli polynomials were defined by
Liu, The generalized central factorial numbers and higher order Norlund Euler- Bernoulli polynomials, (Chinese) Acta Math.