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- Bernoulli_polynomials abstract "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. This is in large part because they are an Appell sequence, i.e. a Sheffer sequence for the ordinary derivative operator. Unlike orthogonal polynomials, the Bernoulli polynomials are remarkable in that the number of crossings of the x-axis in the unit interval does not go up as the degree of the polynomials goes up. In the limit of large degree, the Bernoulli polynomials, appropriately scaled, approach the sine and cosine functions.This article also discusses the Bernoulli polynomials and the related Euler polynomials, and the Bernoulli and Euler numbers.".
- Bernoulli_polynomials thumbnail Bernoulli_polynomials.svg?width=300.
- Bernoulli_polynomials wikiPageExternalLink page_804.htm.
- Bernoulli_polynomials wikiPageID "228161".
- Bernoulli_polynomials wikiPageLength "14989".
- Bernoulli_polynomials wikiPageOutDegree "56".
- Bernoulli_polynomials wikiPageRevisionID "704938357".
- Bernoulli_polynomials wikiPageWikiLink Abramowitz_and_Stegun.
- Bernoulli_polynomials wikiPageWikiLink Appell_sequence.
- Bernoulli_polynomials wikiPageWikiLink Bernoulli_number.
- Bernoulli_polynomials wikiPageWikiLink Category:Number_theory.
- Bernoulli_polynomials wikiPageWikiLink Category:Polynomials.
- Bernoulli_polynomials wikiPageWikiLink Category:Special_functions.
- Bernoulli_polynomials wikiPageWikiLink Derivative.
- Bernoulli_polynomials wikiPageWikiLink Derrick_Henry_Lehmer.
- Bernoulli_polynomials wikiPageWikiLink Dirichlet_series.
- Bernoulli_polynomials wikiPageWikiLink Euler_number.
- Bernoulli_polynomials wikiPageWikiLink Euler–Maclaurin_formula.
- Bernoulli_polynomials wikiPageWikiLink Faulhabers_formula.
- Bernoulli_polynomials wikiPageWikiLink Finite_difference.
- Bernoulli_polynomials wikiPageWikiLink Formal_power_series.
- Bernoulli_polynomials wikiPageWikiLink Fourier_series.
- Bernoulli_polynomials wikiPageWikiLink Fractional_part.
- Bernoulli_polynomials wikiPageWikiLink Generating_function.
- Bernoulli_polynomials wikiPageWikiLink Hermite_polynomials.
- Bernoulli_polynomials wikiPageWikiLink Hurwitz_zeta_function.
- Bernoulli_polynomials wikiPageWikiLink Integral_transform.
- Bernoulli_polynomials wikiPageWikiLink Joseph_Ludwig_Raabe.
- Bernoulli_polynomials wikiPageWikiLink Legendre_chi_function.
- Bernoulli_polynomials wikiPageWikiLink Mathematics.
- Bernoulli_polynomials wikiPageWikiLink Mercator_series.
- Bernoulli_polynomials wikiPageWikiLink Monomial.
- Bernoulli_polynomials wikiPageWikiLink Multiplication_theorem.
- Bernoulli_polynomials wikiPageWikiLink Nörlund–Rice_integral.
- Bernoulli_polynomials wikiPageWikiLink Orthogonal_polynomials.
- Bernoulli_polynomials wikiPageWikiLink Pochhammer_symbol.
- Bernoulli_polynomials wikiPageWikiLink Polynomial_sequence.
- Bernoulli_polynomials wikiPageWikiLink Representation_(mathematics).
- Bernoulli_polynomials wikiPageWikiLink Riemann_zeta_function.
- Bernoulli_polynomials wikiPageWikiLink Sawtooth_wave.
- Bernoulli_polynomials wikiPageWikiLink Series_(mathematics).
- Bernoulli_polynomials wikiPageWikiLink Sheffer_sequence.
- Bernoulli_polynomials wikiPageWikiLink Special_functions.
- Bernoulli_polynomials wikiPageWikiLink Stirling_numbers_of_the_first_kind.
- Bernoulli_polynomials wikiPageWikiLink Stirling_numbers_of_the_second_kind.
- Bernoulli_polynomials wikiPageWikiLink Stirling_polynomials.
- Bernoulli_polynomials wikiPageWikiLink Sun_Zhiwei.
- Bernoulli_polynomials wikiPageWikiLink Trigonometric_functions.
- Bernoulli_polynomials wikiPageWikiLink Umbral_calculus.
- Bernoulli_polynomials wikiPageWikiLink Unit_interval.
- Bernoulli_polynomials wikiPageWikiLink File:Bernoulli_polynomials.svg.
- Bernoulli_polynomials wikiPageWikiLinkText "Bernoulli polynomial".
- Bernoulli_polynomials wikiPageWikiLinkText "Bernoulli polynomials".
- Bernoulli_polynomials wikiPageWikiLinkText "Bernoulli polynomials#Periodic Bernoulli polynomials".
- Bernoulli_polynomials first "K.".
- Bernoulli_polynomials id "24".
- Bernoulli_polynomials last "Dilcher".
- Bernoulli_polynomials title "Bernoulli and Euler Polynomials".
- Bernoulli_polynomials wikiPageUsesTemplate Template:=.
- Bernoulli_polynomials wikiPageUsesTemplate Template:Apostol_IANT.
- Bernoulli_polynomials wikiPageUsesTemplate Template:Cite_book.
- Bernoulli_polynomials wikiPageUsesTemplate Template:Cite_journal.
- Bernoulli_polynomials wikiPageUsesTemplate Template:Dlmf.
- Bernoulli_polynomials wikiPageUsesTemplate Template:Math.
- Bernoulli_polynomials subject Category:Number_theory.
- Bernoulli_polynomials subject Category:Polynomials.
- Bernoulli_polynomials subject Category:Special_functions.
- Bernoulli_polynomials type Type.
- Bernoulli_polynomials type Combinatoric.
- Bernoulli_polynomials type Field.
- Bernoulli_polynomials type Function.
- Bernoulli_polynomials type Polynomial.
- Bernoulli_polynomials type Redirect.
- Bernoulli_polynomials type Type.
- Bernoulli_polynomials comment "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. This is in large part because they are an Appell sequence, i.e. a Sheffer sequence for the ordinary derivative operator. Unlike orthogonal polynomials, the Bernoulli polynomials are remarkable in that the number of crossings of the x-axis in the unit interval does not go up as the degree of the polynomials goes up.".
- Bernoulli_polynomials label "Bernoulli polynomials".
- Bernoulli_polynomials sameAs Q2346201.
- Bernoulli_polynomials sameAs Polinomis_de_Bernoulli.
- Bernoulli_polynomials sameAs Polinomios_de_Bernoulli.
- Bernoulli_polynomials sameAs Polynôme_de_Bernoulli.
- Bernoulli_polynomials sameAs Polinomio_di_Bernoulli.
- Bernoulli_polynomials sameAs ベルヌーイ多項式.
- Bernoulli_polynomials sameAs Euler-polynoom.
- Bernoulli_polynomials sameAs Polinòmi_ëd_Bernoulli.
- Bernoulli_polynomials sameAs m.01h6y5.
- Bernoulli_polynomials sameAs Многочлены_Бернулли.
- Bernoulli_polynomials sameAs Бернулијеви_полиноми.
- Bernoulli_polynomials sameAs Bernoullipolynom.
- Bernoulli_polynomials sameAs Многочлени_Бернуллі.
- Bernoulli_polynomials sameAs Q2346201.
- Bernoulli_polynomials sameAs 伯努利多項式.
- Bernoulli_polynomials wasDerivedFrom Bernoulli_polynomials?oldid=704938357.
- Bernoulli_polynomials depiction Bernoulli_polynomials.svg.
- Bernoulli_polynomials isPrimaryTopicOf Bernoulli_polynomials.