Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-05-14T01:32:13.256Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Polynomials of Touchard Connected with the Bernoulli Numbers

Published online by Cambridge University Press:  20 November 2018

Leonard Carlitz
Leonard Carlitz*
Affiliation:
Duke University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In a recent paper (4) Touchard has constructed a set of polynomials Ωn(z) such that

(1),

where after expansion of the left member Bm is replaced by Bm,

,

and

(2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 188 - 190
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Bateman, H., Some properties of a certain set of polynomials, Töhoku Math. J., 87 (1933), 23–38.Google Scholar
2. Bateman, H., The polynomial Fn(x), Ann. Math., 35 (1934), 767–775.Google Scholar
3. Nôrlund, N. E., Vorlesungen über Differenzenrechnung (Berlin, 1924).Google Scholar
4. Touchard, J., Nombres exponentiels et nombres de Bernoulli, Can. J. Math., 8 (1956), 305–320.Google Scholar
5. Wyman, M. and Moser, L., On some polynomials of Touchard, Can. J. Math., 8 (1956), 321–326.Google Scholar