Talk:Umbral calculus

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Is this the same thing as selector calculus? —Keenan Pepper 21:42, 24 June 2006 (UTC)

It could well be related, but there's not enough information in that article to be sure. Michael Hardy 23:45, 24 June 2006 (UTC)

This article has a big problem with NPOV —Preceding unsigned comment added by 76.184.81.125 (talk) 17:45, 31 July 2009 (UTC)

Please be specific. Comments with no specificity don't help. Michael Hardy (talk) 20:57, 31 July 2009 (UTC)

If you mean saying the old umbral calculus was ad hoc, that there was a failed attempt to fix it and later it was done properly, then the survey in the pdf in the externals is good on that and I certainly think it is fair description. Dmcq (talk) 06:32, 16 August 2009 (UTC)

The modern umbral calculus

The computation there makes no sense (or is very badly explained). Is there any relation between B_n(x) and L(something) when x is nonzero?--Blaisorblade (talk) 20:46, 15 January 2013 (UTC)

Apologies, now I got it, I didn't recognize that one step was just expanding a Bernoulli polynomial. Still, there was no example of why the calculation provided motivates the computation. So I proved the expansion relation for Bernoulli polynomials. Note that I made it up after reading a bit on http://www.romanpress.com/MathArticles/TheoryI.pdf, where I just learned again on linear operators. Still, I trust you can check the proof - write me a message if it doesn't work, so that I get notified.--Blaisorblade (talk) 22:10, 15 January 2013 (UTC)

not absurd

Taking indices as exponents is not absurd: in the case of one variable and P-finite sequences, a_n is the constant term of diffⁿ(A), with diff the differential operator and A the generating function of a. The concept is readily applied to several variables, e.g. Riordan arrays. --SCIdude (talk) 16:09, 6 February 2014 (UTC)

Remove flowery confusing language

Terms like “proof” and “shadowy” should be removed, and instead stick to a clear explanation of what umbral calculus is. I think the entire introduction is confusing. Reading it I gain zero intuition. Something shouldn’t be portrayed as mystical, magical or something that defies understanding. There just need to be clear statements. 120.21.217.39 (talk) 08:46, 3 August 2022 (UTC)

Your complaint is valid. I tire of a generation of mathematicians who, unlike their predecessors, know nothing of how every piece works perfectly together, yet have undeservingly inherited the respect surrounding the subject. It is truly turning into something of a 'magic' when it should be very plain. The only reasonable explanation is that the teachers no longer have deep understanding, so they complicate things to hide their lack of breadth and depth. It is easy to maintin pretense.

True mathematics is a game where one can do absolutely whatever one wants to do, if one is patient and bright enough.

Calling Leibnitz' branch of calculus, where one is free to (and recommended to) augment functions with extra parameters and integrate and differentiate in a variable or variables that may not be the principal variable - a line of thinking that actually preceded the calculus and is likely older than Viete - calling this very basic method of generation by a modern name just because one is historically ignorant is the height of postmodern arrogance. It makes one realize that people who get these degrees haven't even read the basic originals by Eucid, Gauss, Lagrange, Abel, etc which are readily available in English, not to mention the original works of those who have followed. 129.93.161.205 (talk) 14:41, 8 August 2024 (UTC)