Erratum to: Difference equations. (Recurrence relations)

1991 ◽  
pp. 169-169
Author(s):  
Peter Berck ◽  
Knut Sydsæter
Keyword(s):  
Difference Equations ◽  
Recurrence Relations

scholarly journals The Hermite polynomials and the Bessel functions from a general point of view

2003 ◽  
Vol 2003 (57) ◽  
pp. 3633-3642 ◽  
Author(s):  
G. Dattoli ◽  
H. M. Srivastava ◽  
D. Sacchetti
Keyword(s):  
Difference Equations ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Bessel Functions ◽  
Hermite Polynomials ◽  
Point Of View ◽  
General Point ◽  
Ordinary Case

We introduce new families of Hermite polynomials and of Bessel functions from a point of view involving the use of nonexponential generating functions. We study their relevant recurrence relations and show that they satisfy differential-difference equations which are isospectral to those of the ordinary case. We also indicate the usefulness of some of these new families.

scholarly journals Determinant Forms, Difference Equations and Zeros of the q-Hermite-Appell Polynomials

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 258 ◽  
Author(s):  
Subuhi Khan ◽  
Tabinda Nahid
Keyword(s):  
Generating Function ◽  
Difference Equations ◽  
Recurrence Relations ◽  
Computer Experiment ◽  
Appell Polynomials ◽  
Distribution Of Zeros ◽  
Hybrid Form ◽  
Special Polynomials

The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite-Appell polynomials by means of generating function and series definition. Some significant properties of q-Hermite-Appell polynomials such as determinant definitions, q-recurrence relations and q-difference equations are established. Examples providing the corresponding results for certain members belonging to this q-Hermite-Appell family are considered. In addition, graphs of certain q-special polynomials are demonstrated using computer experiment. Thereafter, distribution of zeros of these q-special polynomials is displayed.

scholarly journals The Chebyshev Difference Equation

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 74
Author(s):  
Tom Cuchta ◽  
Michael Pavelites ◽  
Randi Tinney
Keyword(s):  
Difference Equation ◽  
Differential Equations ◽  
Difference Equations ◽  
Chebyshev Polynomials ◽  
Hypergeometric Series ◽  
Recurrence Relations ◽  
New Class

We define and investigate a new class of difference equations related to the classical Chebyshev differential equations of the first and second kind. The resulting “discrete Chebyshev polynomials” of the first and second kind have qualitatively similar properties to their continuous counterparts, including a representation by hypergeometric series, recurrence relations, and derivative relations.

scholarly journals QUALITATIVE THEORY OF PARTIAL DIFFERENCE EQUATIONS (I): OSCILLATION OF NONLINEAR PARTIAL DIFFERENCE EQUATIONS

1994 ◽  
Vol 25 (3) ◽  
pp. 279-288
Author(s):  
SUI SUN CHENG ◽  
BING-GEN ZHANG
Keyword(s):  
Difference Equations ◽  
Recurrence Relations ◽  
Qualitative Theory ◽  
Partial Difference Equations ◽  
Partial Difference ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Equations With Delay

This paper is concerned with a class of nonlinear partial difference equations with delay. By means of an averaging technique, and several oscillation criteria for ordinary recurrence relations, we are able to establish several oscillation criteria for the partial difference equations.

scholarly journals Apostol Type (p, q)-Frobenius-Euler Polynomials and Numbers

2017 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Difference Equations ◽  
Recurrence Relations ◽  
Integral Representations ◽  
Euler Polynomials ◽  
Addition Theorems ◽  
Explicit Formulas ◽  
Euler Polynomials And Numbers ◽  
Appl Math

In the present paper, we introduce (p, q)-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, explicit formulas and relations for these polynomials and numbers. Moreover, we discover (p, q)-extensions of Carlitz's result [L. Carlitz, Mat. Mag., 32 (1959), 247–260] and Srivastava and Pintér addition theorems in [H. M. Srivastava, A. Pinter, Appl. Math. Lett., 17 (2004), 375–380].

scholarly journals Certain Results on (p,q)-Hermite Based Apostol Type Frobenius-Euler Polynomials

2019 ◽  
Author(s):  
Waseem Khan ◽  
Idrees Ahmad Khan ◽  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Difference Equations ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Integral Representations ◽  
Euler Polynomials ◽  
Addition Theorems ◽  
Summation Formulas ◽  
Euler Polynomials And Numbers

In the present paper, the (p,q)-Hermite based Apostol type Frobenius-Euler polynomials and numbers are firstly considered and then diverse basic identities and properties for the mentioned polynomials and numbers, including addition theorems, difference equations, integral representations, derivative properties, recurrence relations. Moreover, we provide summation formulas and relations associated with the Stirling numbers of the second kind.

scholarly journals A class of big (p,q)-Appell polynomials and their associated difference equations

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3085-3121
Author(s):  
H.M. Srivastava ◽  
B.Y. Yaşar ◽  
M.A. Özarslan
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Recurrence Relation ◽  
Difference Equations ◽  
Recurrence Relations ◽  
Bernoulli Polynomials ◽  
Equivalence Theorem ◽  
Euler Polynomials ◽  
Appell Polynomials ◽  
Special Case

In the present paper, we introduce and investigate the big (p,q)-Appell polynomials. We prove an equivalance theorem satisfied by the big (p, q)-Appell polynomials. As a special case of the big (p,q)- Appell polynomials, we present the corresponding equivalence theorem, recurrence relation and difference equation for the big q-Appell polynomials. We also present the equivalence theorem, recurrence relation and differential equation for the usual Appell polynomials. Moreover, for the big (p; q)-Bernoulli polynomials and the big (p; q)-Euler polynomials, we obtain recurrence relations and difference equations. In the special case when p = 1, we obtain recurrence relations and difference equations which are satisfied by the big q-Bernoulli polynomials and the big q-Euler polynomials. In the case when p = 1 and q ? 1-, the big (p,q)-Appell polynomials reduce to the usual Appell polynomials. Therefore, the recurrence relation and the difference equation obtained for the big (p; q)-Appell polynomials coincide with the recurrence relation and differential equation satisfied by the usual Appell polynomials. In the last section, we have chosen to also point out some obvious connections between the (p; q)-analysis and the classical q-analysis, which would show rather clearly that, in most cases, the transition from a known q-result to the corresponding (p,q)-result is fairly straightforward.

scholarly journals Discrete Hypergeometric Legendre Polynomials

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2546
Author(s):  
Tom Cuchta ◽  
Rebecca Luketic
Keyword(s):  
Generating Function ◽  
Difference Equations ◽  
Legendre Polynomials ◽  
Hypergeometric Series ◽  
Recurrence Relations ◽  
Discrete Analog

A discrete analog of the Legendre polynomials defined by discrete hypergeometric series is investigated. The resulting polynomials have qualitatively similar properties to classical Legendre polynomials. We derive their difference equations, recurrence relations, and generating function.

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