On a new general method of summation
Classical Analysis and ODEs
2011-10-26 v2 Mathematical Physics
math.MP
Number Theory
Abstract
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation formulas, and assigns limits to certain unbounded or oscillating functions. Some problems and future lines of research are briefly discussed.
Cite
@article{arxiv.1105.2787,
title = {On a new general method of summation},
author = {Armen Bagdasaryan},
journal= {arXiv preprint arXiv:1105.2787},
year = {2011}
}
Comments
32 pages, amsart style; misprints corrected; in section 4, added propositions 4.14, 4.32 and remark 4.16 concerning Bernoulli numbers and remark 4.31; in section 6, added a paragraph on factorial function; some other minor additions throughout the text