Combinatorics | Polynomials | Finite differences

Umbral calculus

In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain "shadowy" techniques used to "prove" them. These techniques were introduced by John Blissard and are sometimes called Blissard's symbolic method. They are often attributed to Édouard Lucas (or James Joseph Sylvester), who used the technique extensively. (Wikipedia).

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From playlist Summer of Math Exposition Youtube Videos

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Pidduck polynomials | Vector space | Recursion | James Joseph Sylvester | Derivative | Symbolic method | Differential calculus | Sheffer sequence | Electronic Journal of Combinatorics | Finite difference | Polynomial | Combinatorics | Algebra over a field | Polynomial sequence | Binomial type | Appell sequence | Narumi polynomials | Bernoulli polynomials | Binomial coefficient | Mathematics | Partition of a set | Bernoulli umbra | Taylor series | Faulhaber's formula | Equivalence relation | Édouard Lucas | Real-valued function | Cumulant