Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T10:00:10.221Z Has data issue: false hasContentIssue false
  • English
  • Français

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
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.

We consider the product of two power series with positive coefficients: .

What conditions will ensure that the coefficients wn shall be either (i) monotonic, or (ii) logarithmically convex? By the latter, we mean that wn2 ≤ Wn-1Wn+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 un, vn to certain binomial coefficients, rather than in terms of un, vn themselves.

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.