Tag Archives: Appell raising operators

Reps of the lowering / destruction / annihilation operator for binomial Sheffer polynomial sequences

Posted on June 30, 2023 by Tom Copeland

Just posted a belated response concerning these reps to the question “Trying to characterize an ;umbral shift‘” on Math Stack Exchange posted by the creator of the YouTube video The Shadowy World of Umbral Calculus. The analysis includes a presentation … Continue reading →

Posted in Math | Tagged annihilation operator, Appell raising operators, Appell Sheffer polynomial sequences, Bernoulli polynomials, binomial Sheffer polynomial sequences, conjugation of derivative operator, destruction operator, Differential operators, Exponential generating functions, lowering operator, operational calculus, reciprocal integers, Stirling numbers of the first kind, Stirling numbers of the second kind, Todd operator, Umbral calculus, Umbral composition, umbral inverses, umbral substitution operators | Leave a comment

Calculus, Combinatorics, and Geometry Underlying OEIS A060540, and the Exponential Formula

Posted on June 12, 2021 by Tom Copeland

The pdf below gives the associations of OEIS A060540 with the operator calculus of Appell Sheffer polynomials, the combinatorics of simple set partitions encoded in the Faa di Bruno formula for composition of analytic functions (formal Taylor series), and the … Continue reading →

Posted in Math | Tagged Appell raising operators, Appell Sheffer polynomial sequences, compositional partition polynomials, Differential operators, Exponential formula, Faa di Bruno partition polynomials, hypertetrahedra, hypertriangles, n-simplices, OEIS 036040, OEIS A060540, Set partitions | 3 Comments

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Tag Archives: Appell raising operators

Reps of the lowering / destruction / annihilation operator for binomial Sheffer polynomial sequences

Calculus, Combinatorics, and Geometry Underlying OEIS A060540, and the Exponential Formula

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