Results 161 to 170 of about 166,207 (201)
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SIAM Journal on Mathematical Analysis, 1994
A rigorous presentation of the umbral calculus, as formerly applied heuristically by Blissard, Bell, Riordan, and others is given. As an application, the basic identities for Bernoulli numbers, as well as their generalizations first developed by Norlund are derived.
Gian-Carlo Rota, B. D. Taylor
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A rigorous presentation of the umbral calculus, as formerly applied heuristically by Blissard, Bell, Riordan, and others is given. As an application, the basic identities for Bernoulli numbers, as well as their generalizations first developed by Norlund are derived.
Gian-Carlo Rota, B. D. Taylor
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Umbral Calculus in Hilbert Space
1998No abstract.
Alessandro Di Bucchianico +2 more
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Some identities of the q-Laguerre polynomials on q-Umbral calculus
, 2017Some interesting identities of Sheffer polynomials was given by Roman [11], [12]. In this paper, we study a q-analogue of Laguerre polynomials which are also q-Sheffer polynomials. Furthermore, we give some new properties and formulas of these q-Laguerre
R. Dere
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Guide to the Umbral Calculus - A Different Mathematical Language
Guide to the Umbral Calculus, 2022S. Licciardi, G. Dattoli
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Symmetric q-extension of $$\lambda $$ λ -Apostol–Euler polynomials via umbral calculus
Indian journal of pure and applied mathematics, 2022H. Elmonser
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The umbral calculus on logarithmic algebras
Acta Applicandae Mathematicae, 1990D. E. Loeb and G.-C. Rota, using the operator of differentiation D, constructed the logarithmic algebra that is the generalization of the algebra of formal Laurent series. They also introduced Appell graded logarithmic sequences and binomial (basic) graded logarithmic sequences as sequences of elements of the logarithmic algebra and extended the main ...
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Natural Exponential Families and Umbral Calculus
1998We use the Umbral Calculus to investigate the relation between natural exponential families and Sheffer polynomials. As a corollary, we obtain a new transparent proof of Feinsilver’s theorem which says that natural exponential families have a quadratic variance function if and only if their associated Sheffer polynomials are orthogonal.
A. Di Bucchianico, D.E. Loeb
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Rota?s umbral calculus and recursions
Algebra Universalis, 2003Umbral Calculus can provide exact solutions to a wide range of linear recursions. We summarize the relevant theory and give a variety of examples from combinatorics in one, two and three variables.
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Frobenius Endomorphisms in the Umbral Calculus
Studies in Applied Mathematics, 1980Frobenius operators Fn are introduced on sequences of binomial type. The Laguerre polynomials are essentially characterized by the property that Fn coincides with n‐fold binomial convolution.
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The umbral calculus and orthogonal polynomials
Acta Applicandae Mathematicae, 1990We determine all orthogonal polynomials having Boas-Buck generating functions g(t)Ψ(xf(t)), where % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr ...
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