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Asymptotic Expansions

Published online by Cambridge University Press:  20 November 2018

Leo Moser  and
Max Wyman
Leo Moser
Affiliation:
University of Alberta
Max Wyman
Affiliation:
University of Alberta
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1. Introduction. Let a1 a2, …, am be a set of real non-negative numbers and let

1.1 P(x) = a1x + a2x2 + … + amxm (am ≠ 0).

Many combinatorial problems can be reduced to the study of numbers Bn generated by

1.2.

Some problems of this type were treated by Touchard (7), Jacobsthal (3), Chowla, Herstein, Moore and Scott (1; 2), and the present authors (4).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 225 - 233
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Chowla, S., Herstein, I. N., and Moore, K., On recursions connected with symmetric groups I, Can. J. Math., 8 (1951), 328–334.Google Scholar
2. Chowla, S., Herstein, I. N., and Scott, W. R., The solutions of xd = 1 in symmetric groups, Norske Vid. Selsk., 25 (1952), 29–31.Google Scholar
3. Jabobsthal, E., Sur le nombre d'éléments du group symmetrique Sn dont Vordre est un nombre premier, Norske Vid. Selsk., 21 (1949), 49–51.Google Scholar
4. Moser, L. and Wyman, M., On solutions of xd = 1 in symmetric groups, Can. J. Math., 7 (1955), 159–168.Google Scholar
5. Pólya, G., Ueber die Nullstellen sukzessiver Derivierten, Math. Z., 12 (1922), 36–60.Google Scholar
6. Szegö, G., Orthogonal Polynomials, Amer. Math. Soc. Coll. Publications (New York, 1939).Google Scholar
7. Touchard, J., Sur les cycles des substitutions, Acta Math., 70 (1939), 242–297.Google Scholar