The forum discussion revolves around a paper titled "A Simple Continuation for Partial Sums," recently accepted by ArXiV. The author seeks constructive criticism to enhance the clarity and rigor of their mathematical arguments, particularly regarding the definitions of variables such as f, k, n, and L. Key feedback includes the necessity of defining these variables early in the paper, addressing convergence conditions for the infinite series, and ensuring that the notation adheres to established mathematical conventions. The discussion highlights the importance of clarity in theoretical mathematics writing, especially for publishable work.
PREREQUISITESMathematicians, academic writers, and researchers in theoretical mathematics seeking to improve their writing clarity and rigor, particularly those preparing papers for publication.
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. :)