Unimodal sequences show Lambert W is Bernstein
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2010
- DOI:
- arXiv:
- arXiv:1011.5940
- Bibcode:
- 2010arXiv1011.5940K
- Keywords:
-
- Mathematics - Classical Analysis and ODEs;
- 11B83
- E-Print:
- 6 pages