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On The Product of Two Power Series

Published online by Cambridge University Press:  20 November 2018

H. Davenport  and
G. Pôlya
H. Davenport
Affiliation:
University College, London
G. Pôlya
Affiliation:
Stanford University
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We consider the product of two power series with positive coefficients: .

What conditions will ensure that the coefficients w n shall be either (i) monotonic, or (ii) logarithmically convex? By the latter, we mean that wn2 ≤ W n-1 W n+1 for n = 1, 2, … In investigating this question, which was suggested by a special example, we have found it convenient to express the conditions in terms of the ratios of u n , v n to certain binomial coefficients, rather than in terms of u n , v n themselves.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 1 , Issue 1 , 01 February 1949 , pp. 1 - 5
Copyright
Copyright © Canadian Mathematical Society 1949

References

1 lMath. ZeiL, vol. 28 (1928), 161-170.