Euler Polynomials and Combinatoric Convolution Sums of Divisor Functions with Even Indices

Daeyeoul Kim, Abdelmejid Bayad, Joongsoo Park
2014 Abstract and Applied Analysis  
We study combinatoric convolution sums of certain divisor functions involving even indices. We express them as a linear combination of divisor functions and Euler polynomials and obtain identitiesD2k(n)=(1/4)σ2k+1,0(n;2)-2·42kσ2k+1(n/4) -(1/2)[∑d|n,d≡1 (4){E2k(d)+E2k(d-1)}+22k∑d|n,d≡1 (2)E2k((d+(-1)(d-1)/2)/2)],U2k(p,q)=22k-2[-((p+q)/2)E2k((p+q)/2+1)+((q-p)/2)E2k((q-p)/2)-E2k((p+1)/2)-E2k((q+1)/2)+E2k+1((p+q)/2+1)-E2k+1((q-p)/2)], andF2k(n)=(1/2){σ2k+1†(n)-σ2k†(n)}. As applications of these
more » ... ations of these identities, we give several concrete interpretations in terms of the procedural modelling method.
doi:10.1155/2014/289187 fatcat:mczybk3swjfwhmsgzvh2tbetve