On a new general method of summation
arXiv:1105.2787
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.
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