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mathematical physics > special function > Bernoulli polynomial
mathematical analysis > functional analysis > special function > Bernoulli polynomial
mathematical analysis > function > elementary function > polynomial > Bernoulli polynomial
algebra > polynomial > Bernoulli polynomial
number > number theory > analytic number theory > Bernoulli polynomial

Terme préférentiel

Bernoulli polynomial  

Définition(s)

  • In mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, combine the Bernoulli numbers and binomial coefficients. They are used for series expansion of functions, and with the Euler–MacLaurin formula. These polynomials occur in the study of many special functions and, in particular, the Riemann zeta function and the Hurwitz zeta function. They are an Appell sequence (i.e. a Sheffer sequence for the ordinary derivative operator). For the Bernoulli polynomials, the number of crossings of the x-axis in the unit interval does not go up with the degree. In the limit of large degree, they approach, when appropriately scaled, the sine and cosine functions.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Bernoulli_polynomials)

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http://data.loterre.fr/ark:/67375/PSR-SWKNH69B-F

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RDF/XML TURTLE JSON-LD Date de création 16/08/2023, dernière modif. 22/09/2023