Umbral Calculus
Barnes type Peters polynomial with umbral calculus viewpoint
... use umbral calculus to obtain several new and interesting identi- ties of Barnes-type Peters ...polynomials. Umbral calculus has been used in numerous prob- lems of mathematics (for example, ...
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On Poly Bernoulli polynomials of the second kind with umbral calculus viewpoint
... Poly-Bernoulli polynomials of the second kind were introduced in Kim et al. (Adv. Differ. Equ. 2014:219, 2014) as a generalization of the Bernoulli polynomial of the second kind. Here we investigate those polynomials and ...
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Some identities of q Euler polynomials arising from q umbral calculus
... of umbral calculus (see (Araci et ...q-umbral calculus due to Roman, and we study a new q-extension of Euler numbers and polynomials which are derived from q-umbral ...
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Extended p adic q invariant integrals on Zp associated with applications of umbral calculus
... of umbral algebra to special functions in ...of umbral calculus for Frobenius-Euler polynomials [] and Euler polynomials ...of umbral calculus associated with p-adic invariants ...
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Applications of q-Umbral Calculus to Modi ed Apostol Type q-Bernoulli Polynomials
... Abstract- This article aims to identify the generating function of modi…ed Apostol type q-Bernoulli poly- nomials. With the aid of this generating function, some properties of modi…ed Apostol type q-Bernoulli polynomials ...
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Some properties of higher order Daehee polynomials of the second kind arising from umbral calculus
... the algebra of the formal power series in t and the vector space of all linear functionals on P, and so an element f (t) of F will be thought of as both a formal power series and a linear functional. We call F the ...
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Some identities of Bernoulli, Euler and Abel polynomials arising from umbral calculus
... So, F denotes both the algebra of formal power series in t and the vector space of all linear functionals on P, and so an element f (t) of F is thought of as both a formal power series and a linear functional (see ...
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Poly Cauchy numbers and polynomials of the second kind with umbral calculus viewpoint
... is a vector space isomorphism from P ∗ onto F . Henceforth, F denotes both the algebra of formal power series in t and the vector space of all linear functionals on P, and so an element f (t) of F will be thought of as ...
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Some identities of higher order Bernoulli, Euler, and Hermite polynomials arising from umbral calculus
... In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler, and Hermite polynomials ...
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Frobenius Euler polynomials and umbral calculus in the p adic case
... Here, F denotes both the algebra of formal power series in t and the vector space of all linear functionals on P , and so an element f (t) of F will be thought of as both a formal power series and a linear functional ...
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Degenerate poly Bernoulli polynomials with umbral calculus viewpoint
... use umbral calculus to obtain several new and interesting identities of degenerate poly-Bernoulli ...the umbral cal- culus as given in [, ...
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Extended r central Bell polynopmials with umbral calculus viewpoint
... Here we will derive some properties, identities and recurrence relations for the extended r- central Bell polynomials by making use of umbral calculus techniques and the formulas in Sect. 2. In addition, we ...
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Apostol Euler polynomials arising from umbral calculus
... Kim et al Advances in Difference Equations 2013, 2013 301 http //www advancesindifferenceequations com/content/2013/1/301 R ES EARCH Open Access Apostol Euler polynomials arising from umbral calculus[.] ...
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Some new identities of Bernoulli, Euler and Hermite polynomials arising from umbral calculus
... Kim et al Advances in Difference Equations 2013, 2013 73 http //www advancesindifferenceequations com/content/2013/1/73 R ES EA RCH Open Access Some new identities of Bernoulli, Euler and Hermite poly[.] ...
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Some identities of Frobenius Euler polynomials arising from umbral calculus
... Kim and Kim Advances in Difference Equations 2012, 2012 196 http //www advancesindifferenceequations com/content/2012/1/196 R ES EA RCH Open Access Some identities of Frobenius Euler polynomials arisi[.] ...
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Probabilistic Proofs of Some Relationships Between the Bernoulli and Euler Polynomials
... Remark 8. The underlying principle of the approach involved in Remarks 6 and 7 (and leading to Theorem 3 above) is that any Bernoulli or Euler polynomial can be represented as a moment of a shifted monomial as (for ...
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Powers under umbral composition and degeneration for Sheffer sequences
... use umbral calculus and to study powers under umbral compo- sition and degeneration for Sheffer ...sequences. Umbral calculus (see [, ]) has been used in numerous problems of applied ...
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A note on some identities of derangement polynomials
... The umbral calculus comes under the heading of combinatorics, the calculus of finite differences, the theory of special functions, and formal solutions to differential ...
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Degenerate poly Cauchy polynomials with a q parameter
... use umbral calculus techniques (see [, ]) in order to de- rive some properties, recurrence relations, and identities for the degenerate poly-Cauchy polynomials with a q parameter of the first kind and of ...
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Transreal Calculus
... Abstract—Transreal arithmetic totalises real arithmetic by defining division by zero in terms of three definite, non-finite numbers: positive infinity, negative infinity and nullity. We describe the transreal tangent ...
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