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 (1861) and are sometimes called Blissard's symbolic method. They are often attributed to Édouard Lucas (or James Joseph Sylvester), who used the technique extensively.

In the 1930s and 1940s, Eric Temple Bell attempted to set the umbral calculus on a rigorous footing.

In the 1970s, Steven Roman, Gian-Carlo Rota, and others developed the umbral calculus by means of linear functionals on spaces of polynomials. Currently, umbral calculus refers to the study of Sheffer sequences, including polynomial sequences of binomial type and Appell sequences, but may encompass in its penumbra systematic correspondence techniques of the calculus of finite differences.

Read more about Umbral CalculusThe 19th-century Umbral Calculus, Umbral Taylor Series, Bell and Riordan, The Modern Umbral Calculus

Other articles related to "umbral calculus, umbral":

The Modern Umbral Calculus
... In a paper published in 1964, Rota used umbral methods to establish the recursion formula satisfied by the Bell numbers, which enumerate partitions of finite sets ... In the paper of Roman and Rota cited below, the umbral calculus is characterized as the study of the umbral algebra, defined as the algebra of linear functionals on the vector space of ... Rota later applied umbral calculus extensively in his paper with Shen to study the various combinatorial properties of the cumulants ...

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