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.
A general interpolating formula and error bounds
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.
Some another remarks on the generalization of Bernoulli and Euler numbers
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.
Some indefinite integrals involving certain polynomial
The essential ingredients of the recipe are the Bernoulli polynomials and their relatives.
Terao, The Shi arrangements and the Bernoulli polynomials, Bull.
The Shi arrangement of the type [D.sub.l]
For some details on the Bernoulli polynomials and the Bernoulli numbers, see for example (8), (9).
Improvements and generalizations of some Euler Gruss type inequalities and applications
Qi in [11] and [13]-[15], defined the generalization of Bernoulli polynomials as
Generalizations on poly-Eulerian numbers and polynomials
In the usual notation, the n-th Bernoulli polynomials were defined by
A note on multiple L-function
Liu, The generalized central factorial numbers and higher order Norlund Euler- Bernoulli polynomials, (Chinese) Acta Math.
Recurrence formulas for the generalized Euler numbers [E.sup.(k)1.sub.2n]>
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