Talk:Umbral calculus

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)