The discussion revolves around a paper titled "A Simple Continuation for Partial Sums," recently accepted by ArXiV. Participants provide constructive criticism and seek to clarify various aspects of the paper, including definitions, theorems, and assumptions related to mathematical summation and convergence.
Participants do not reach a consensus on the validity of the paper's results. Multiple competing views are presented, particularly regarding the definitions and implications of Theorem 1, as well as the assumptions made about the function f.
There are limitations regarding the clarity of definitions and assumptions in the paper, particularly concerning the nature of the function f and the conditions under which theorems are stated. The discussion highlights the need for precise language in mathematical writing.
This discussion may be useful for mathematicians, researchers, or students interested in mathematical writing, theorems related to summation, and the nuances of convergence in series.
I didn’t see this edit, I devoted half a subsection on this specific function (the alternating harmonic numbers) and came up with a conjecture on its zeroes and a reflection formula for itfresh_42 said:Another idea is to check functions ##f(k)=\sum_{m=1}^k \dfrac{(-1)^{m+1}}{m}## where ##\lim_{n \to \infty}f(n)## depends on the ordering of the sum.
Maybe something from Ramanujan, but Riemann, Euler, and Maclaurin don't need specific citations, IMO. Every calculus book mentions the Riemann integral and Maclaurin series, as well as Euler's equation involving ##e, \pi, -1, i## and ##0## without citing the work in which these first appeared.sbrothy said:You mention Riemann, Euler, MacLauri and Ramanjuan but don't cite them.
No, there isn't a Riemann integral or Maclaurin series. It's the Riemann zeta function and Euler-Maclaurin formula. But again, these two are pretty well-known already.Mark44 said:Maybe something from Ramanujan, but Riemann, Euler, and Maclaurin don't need specific citations, IMO. Every calculus book mentions the Riemann integral and Maclaurin series, as well as Euler's equation involving ##e, \pi, -1, i## and ##0## without citing the work in which these first appeared.
I gave those as examples, but my point was that these names are so well-known, that citations aren't necessary.mathhabibi said:No, there isn't a Riemann integral or Maclaurin series. It's the Riemann zeta function and Euler-Maclaurin formula. But again, these two are pretty well-known already.
I think I can still cite his notebooks somehow. You have contributed something, don't downplay what you've done :)sbrothy said:I appreciate the little heads-up. Don't worry. I'm under no illusions that I can really contribute anything. All the best. :)