Mathematical Reports - Comptes rendus mathématiques

of the Academy of Science | de l'Académie des sciences

  • Home
  • Articles
  • News
  • Editorial Board
  • General Information
    • General Information
    • Preparation of Manuscripts
    • Subscription Information
    • FAQ
    • Help

unimodal sequence — 1 results found.

      
Show all abstractsHide all abstracts

Unimodal sequences show that Lambert $W$ is Bernstein
C. R. Math. Rep. Acad. Sci. Canada Vol. 33 (2) 2011, pp. 50–56
G.A. Kalugin; D.J. Jeffrey (Received: 2010/11/28)

Show AbstractHide Abstract

We consider a sequence of polynomials appearing in expressions for the derivatives of the Lambert \(W\) function. The coefficients of each polynomial are shown to form a positive sequence that is log-concave and unimodal. This property implies that the positive real branch of the Lambert \(W\) function is a Bernstein function.

Nous considérons une séquence de polynômes que l’on retrouve dans l’expression des dérivées de la fonction Lambert \(W\). Nous montrons que les coefficients de chaque polynôme forment une séquence positive qui est log-concave et unimodale. Cette propriété implique que la branche réelle positive de la fonction Lambert \(W\) est une fonction de Bernstein.

 Volume / Issue

Most used Keywords

algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

Most used AMS

05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F11 11F66 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K14 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F25 39B72 42C05 43A07 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 83C05

Be notified of new issues

Copyright © 2023 · The Royal Society of Canada | La Société royale du Canada · Log in
ISSN: 2816-5810 (Online)