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On Touchard Polynomials

Published online by Cambridge University Press:  20 November 2018

Fred Brafman
Fred Brafman*
Affiliation:
Southern Illinois University, Carbondale
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Wyman and Moser (5) have recently given an explicit form for some polynomials of Touchard (4). Equation (6) of this note will give a simpler expression for these polynomials. Subsequently, generating functions (9) and (12) will be obtained.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 191 - 193
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Bailey, W. N., Generalized Hyper geometric Series, Cambridge Tract No. 32 (1935).Google Scholar
2. Carlitz, L., Some polynomials of Touchard connected with the Bernoulli numbers. Can. J. Math., 9 (1957), 188–190.Google Scholar
3. Chaundy, T. W., An extension of hyper geometric functions, Quart. J. Math., 14 (1943), 55–78.Google Scholar
4. Touchard, Jacques, Nombres exponentiels et nombres de Bernoulli, Can. J. Math., 8 (1956), 305–320.Google Scholar
5. Wyman, Max and Moser, Leo, On some polynomials of Touchard, Can. J. Math., 8 (1956), 321–322.Google Scholar