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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
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Extract

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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