Euler Polynomials and Combinatoric Convolution Sums of Divisor Functions with Even Indices
Joint Authors
Bayad, Abdelmejid
Park, Joongsoo
Kim, Daeyeoul
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-27
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
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 identities D2k(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)], and F2k(n)=(1/2){σ2k+1†(n)-σ2k†(n)}.
As applications of these identities, we give several concrete interpretations in terms of the procedural modelling method.
American Psychological Association (APA)
Kim, Daeyeoul& Bayad, Abdelmejid& Park, Joongsoo. 2014. Euler Polynomials and Combinatoric Convolution Sums of Divisor Functions with Even Indices. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-1033661
Modern Language Association (MLA)
Kim, Daeyeoul…[et al.]. Euler Polynomials and Combinatoric Convolution Sums of Divisor Functions with Even Indices. Abstract and Applied Analysis No. 2014 (2014), pp.1-6.
https://search.emarefa.net/detail/BIM-1033661
American Medical Association (AMA)
Kim, Daeyeoul& Bayad, Abdelmejid& Park, Joongsoo. Euler Polynomials and Combinatoric Convolution Sums of Divisor Functions with Even Indices. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-1033661
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033661