Questions tagged [umbral-calculus]

Umbral calculus refers to a method of formal computation which can be used to prove certain polynomial identities. The term "umbral", meaning "shadowy" in Latin, describes the manner in which the terms in discrete equations (e.g. difference equations) are similar to (or are "shadows of") related terms in power series expansions.

Umbral calculus refers to a method of formal computation which can be used to prove certain polynomial identities. The term "umbral", meaning "shadowy" in Latin, describes the manner in which the terms in discrete equations (e.g. difference equations) are similar to (or are "shadows of") related terms in power series expansions.

25 questions
0
votes
0 answers

What's the intuitive meaning of this relation between volumes of $n$-balls and umbrial calculus?

The volume of an $n$-ball of radius $1$ is $$V_{n}={\frac {\pi ^{n/2}}{\Gamma {\bigl (}{\tfrac {n}{2}}+1{\bigr )}}}.$$ The functional equation of Riemann zeta function is $${\displaystyle \pi ^{-{s \over 2}}\Gamma \left({s \over 2}\right)\zeta…
Anixx
  • 9,119