Evaluation of Sums of Convolved Powers Using Bernoulli Numbers

Application of the discrete polynomials Ki(N - K)jas the approximating functions in conjunction with discrete weighted residual methods [8] leads to evaluation of the sums of convolved powers S(i, j; N) = ∑N K = 0Ki(N - K)j. In this paper, properties of the S(i, j; N) are delineated and the closed-f...

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Bibliographic Details
Published in:SIAM review 1977-01, Vol.19 (1), p.90-99
Main Authors: Neuman, C. P., Schonbach, D. I.
Format: Article
Language:English
Subjects:
Binomials
Coefficients
Difference equations
Electrical engineering
Polynomials
Recursion
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Summary:Application of the discrete polynomials Ki(N - K)jas the approximating functions in conjunction with discrete weighted residual methods [8] leads to evaluation of the sums of convolved powers S(i, j; N) = ∑N K = 0Ki(N - K)j. In this paper, properties of the S(i, j; N) are delineated and the closed-form expression for the sums is derived using Bernoulli numbers.
ISSN:0036-1445
1095-7200
DOI:10.1137/1019006