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A q-operational equation and the Rogers-Szegő polynomials
By solving a q -operational equation with formal power series, we prove a new q -exponential operational identity. This operational identity reveals an...
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Generalized Geometric Polynomials Via Steffensen’s Generalized Factorials and Tanny’s Operators
Our purpose is to give a generalization of geometric polynomials by applying an appropriate linear transformation on the generalized factorial...
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A q-Translation Approach to Liu’s Calculus
We show that there is a concept of q-translation behind the approach used by Liu to prove summation and transformation identities for q-series.We...
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Identities for degenerate Bernoulli polynomials and Korobov polynomials of the first kind
In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices. Then we apply...
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Mittag-Leffler function and fractional differential equations
We adopt a procedure of operational-umbral type to solve the (1 + 1)-dimensional fractional Fokker-Planck equation in which time fractional...
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On supplementary formulas for Sheffer sequences
We study supplementary formulas for Sheffer sequences. As applications of that study, we consider characterizations of Bernoulli, Euler and...
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Some identities of Bell polynomials
We investigate Bell polynomials, also called Touchard polynomials or exponential polynomials, by using and without using umbral calculus. We use...
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Barnes-type Narumi of the second kind and Barnes-type Peters of the second kind hybrid polynomials
In this paper, by considering Barnes-type Narumi polynomials of the second kind and Barnes-type Peters polynomials of the second kind, we define and...
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Barnes-type Peters polynomial with umbral calculus viewpoint
In this paper, we consider the Barnes-type Peters polynomials. We present several explicit formulas and recurrence relations for these polynomials....
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Barnes’ multiple Bernoulli and generalized Barnes’ multiple Frobenius-Euler mixed-type polynomials
In this paper, by considering Barnes’ multiple Bernoulli polynomials as well as generalized Barnes’ multiple Frobenius-Euler polynomials, we define...
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Barnes-type Narumi polynomials
In this paper, we study the Barnes-type Narumi polynomials with umbral calculus viewpoint. From our study, we derive various identities of the...
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Barnes-type Daehee polynomials
In this paper, we consider Barnes-type Daehee polynomials of the first kind and of the second kind. From the properties of the Sheffer sequences of...
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Barnes-type Daehee of the second kind and poly-Cauchy of the second kind mixed-type polynomials
In this paper, we introduce the mixed-type polynomials: Barnes-type Daehee polynomials of the second kind and poly-Cauchy polynomials of the second...
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Barnes-type Daehee of the first kind and poly-Cauchy of the first kind mixed-type polynomials
In this paper, by considering Barnes-type Daehee polynomials of the first kind as well as poly-Cauchy polynomials of the first kind, we define and...
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Barnes’ multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials
In this paper, we consider Barnes’ multiple Frobenius-Euler and poly-Bernoulli mixed-type polynomials. From the properties of Sheffer sequences of...
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q-Bernoulli polynomials and q-umbral calculus
In this paper, we investigate some properties of q -Bernoulli polynomials arising from q -umbral calculus. We find a formula for expressing any...
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Apostol-Euler polynomials arising from umbral calculus
In this paper, by using the orthogonality type as defined in the umbral calculus, we derive an explicit formula for several well-known polynomials as...
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Sheffer sequences of polynomials and their applications
In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our...