Bernoulli and Euler numbers and polynomials
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31: 24.12 Zeros
§24.12(i) Bernoulli Polynomials: Real Zeros
… ►§24.12(iii) Complex Zeros
►For complex zeros of Bernoulli and Euler polynomials, see Delange (1987) and Dilcher (1988). A related topic is the irreducibility of Bernoulli and Euler polynomials. … ►§24.12(iv) Multiple Zeros
…32: 25.2 Definition and Expansions
33: Bibliography D
34: Bibliography B
35: Bibliography H
36: 3.5 Quadrature
Gauss–Legendre Formula
… ►The are the monic Hermite polynomials (§18.3). … ► …37: 3.11 Approximation Techniques
§3.11(i) Minimax Polynomial Approximations
… ► … ►Suppose a function is approximated by the polynomial … ►For splines based on Bernoulli and Euler polynomials, see §24.17(ii). ►For many applications a spline function is a more adaptable approximating tool than the Lagrange interpolation polynomial involving a comparable number of parameters; see §3.3(i), where a single polynomial is used for interpolating on the complete interval . …38: Bibliography E
39: Errata
For consistency we have replaced by .
The generalized hypergeometric function of matrix argument , was linked inadvertently as its single variable counterpart . Furthermore, the Jacobi function of matrix argument , and the Laguerre function of matrix argument , were also linked inadvertently (and incorrectly) in terms of the single variable counterparts given by , and . In order to resolve these inconsistencies, these functions now link correctly to their respective definitions.
Originally all six integrands in these equations were incorrect because their numerators contained the function . The correct function is . The new equations are:
Reported 2016-05-08 by Clemens Heuberger.
Reported 2016-06-27 by Gergő Nemes.
Reported 2016-06-27 by Gergő Nemes.
Originally the term was incorrectly stated as .
Reported 2013-08-01 by Gergő Nemes and subsequently by Nick Jones on December 11, 2013.