Journal of Integer Sequences, Vol. 17 (2014), Article 14.6.7

On an Arithmetic Convolution

Jitender Singh
Department of Mathematics
Guru Nanak Dev University


The Cauchy-type product of two arithmetic functions f and g on nonnegative integers is defined by (fg)(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,    dvi,    ps,    latex    

(Concerned with sequences A027641 A027642 A116419 A116420 A241885 A242225.)

Received April 15 2014; revised versions May 7 2014; May 15 2014. Published in Journal of Integer Sequences, May 19 2014.

Return to Journal of Integer Sequences home page