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The Electronic Journal of Combinatorics, 2021 We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of “magic rules” for lowering and raising indices, through its rebirth in the 1970’s as Rota’s school set it on a firm logical foundation using operator methods, to the current state ...
Andrew Chang
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Journal of Mathematical Analysis and Applications, 1981 AbstractAn algebraic setting for the Roman-Rota umbral calculus is introduced. It is shown how many of the umbral calculus results follow simply by introducing a comultiplication map and requiring it to be an algebra map. The same approach is used to construct a q-umbral calculus.
Ihrig, Edwin C, Ismail, Mourad E.H
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Extended r-central Bell polynopmials with umbral calculus viewpoint
Advances in Difference Equations, 2019 Recently, extended r-central factorial numbers of the second kind and extended r-central Bell polynomials were introduced and various results of them were investigated.
Lee-Chae Jang +3 more
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Some Identities of Fully Degenerate r-Dowling Polynomials Arising from λ-Umbral Calculus
MathematicsThis paper introduces fully Dowling polynomials of the first and second kinds, which are degenerate versions of the ordinary Dowling polynomials. Then, several important identities for these degenerate polynomials are derived.
Xiaoxue Li, Siqi Dong, Yuankui Ma
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Computer algebra and Umbral Calculus [PDF]
Discrete Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anne Bottreau +2 more
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Umbral calculus in positive characteristic [PDF]
Advances in Applied Mathematics, 2005 An umbral calculus over local fields of positive characteristic is developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. Orthonormal bases in the space of continuous $\mathbb F_q$-linear functions are constructed.
Kochubei, Anatoly N.
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SOME IDENTITIES OF FULLY DEGENERATE DOWLING AND FULLY DEGENERATE BELL POLYNOMIALS ARISING FROM λ-UMBRAL CALCULUS [PDF]
Fractals, 2021 Recently, Kim–Kim introduced the [Formula: see text]-umbral calculus, in which the [Formula: see text]-Sheffer sequences occupy the central position. In this paper, we introduce the fully degenerate Bell and the fully degenerate Dowling polynomials, and ...
Yuankui Ma +3 more
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A note on some identities of derangement polynomials. [PDF]
J Inequal Appl, 2018 The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708 (see Carlitz in Fibonacci Q. 16(3):255–258, 1978, Clarke and Sved in Math. Mag. 66(5):299–303, 1993, Kim, Kim and Kwon in Adv. Stud. Contemp. Math. (Kyungshang) 28(1):
Kim T, Kim DS, Jang GW, Kwon J.
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Sheffer-Dunkl Sequences Via Umbral Calculus in the Dunkl Context
Bulletin of the Malaysian Mathematical Sciences SocietyUmbral calculus refers to a series of techniques that can be used to prove some polynomial formulas. Nowadays, it mostly involves the study of Sheffer sequences.
Juan Luis Varona +2 more
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Applications of the classical umbral calculus [PDF]
Algebra Universalis, 2003 34 ...
Ira M Gessel
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