On an Arithmetic Convolution
Department of Mathematics
Guru Nanak Dev University
The Cauchy-type product of two arithmetic functions f and
g on nonnegative integers is defined by (f •
g)(k) := Σ m=0k
C(k, m) f(m)g(k-m). We explore
some algebraic properties of the aforementioned convolution, which is a
fundamental characteristic of the identities involving the Bernoulli
numbers, the Bernoulli polynomials, the power sums, the sums of
products, and so forth.
Full version: pdf,
(Concerned with sequences
Received April 15 2014;
revised versions May 7 2014; May 15 2014.
Published in Journal of Integer Sequences, May 19 2014.
Journal of Integer Sequences home page