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Periodic Generalized Birkhoff Solutions and Farey Intervals for Monotone Recurrence Relations
The aim of this paper is to extend the results associated with periodic orbits from two-dimensions to higher-dimensions. Because of the one-to-one...
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q-Difference Recurrence Relations of Aleph Function with Generalization to nth Derivative
Sharma and Jain studied the basic analogue of Meijer’s G-function by using the methods of q -calculus and constructed the q -difference operators and...
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Solving Third-Order Linear Recurrence Relations with Applications to Number Theory and Combinatorics
In this paper we develop a novel matrix method for solving linear recurrence relations and present explicit formulae for the general solution of the...
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Recurrence relations, associated formulas, and combinatorial sums for some parametrically generalized polynomials arising from an analysis of the Laplace transform and generating functions
The aim of this paper is to obtain some interesting infinite series representations for the Apostol-type parametrically generalized polynomials with...
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Recurrence Equations and Their Closed-Form Solutions
In so-called “divide and conquer” algorithms one usually ends up with a recurrence relation (i.e., inductive or recursive definition!) that defines...
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The Recurrence Case in One Variable
A D-finite sequence is uniquely determined by a recurrence it satisfies and a suitable number of initial terms.
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On a family of higher order recurrence relations: symmetries, formula solutions, periodicity and stability analysis
In this paper, we present formula solutions of a family of difference equations of higher order. We discuss the periodic nature of the solutions and...
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Generating Functions and Recurrence Relations
We usually seek a closed form of G(x). We do not worry about the convergence of the power series since we are primarily interested in x as a formal...
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Recurrence Legendre Polynomials
AbstractThe recurrence polynomials partly orthogonal with respect to Lebesgue measure on the segment symmetric with respect to the unit circle are...
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Forecasting with Using Quasilinear Recurrence Equation
We developed a new approach to the analysis of time series based on the use of quasi-linear recurrence relations. Unlike neural networks, this...
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Some relations on the degenerate Korobov polynomials and poly-Korobov polynomials
In last ten years, many mathematicians ([
4 ,8 –16 ]) studied and investigated for the Korobov polynomials. In this work, we consider the poly-Korobov... -
Recurrence Relations of Poly-Cauchy Numbers by the r-Stirling Transform
We give some formulas of poly-Cauchy numbers by the r -Stirling transform. In the case of the classical or poly-Bernoulli numbers, the formulas are...
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On Relations between Harmonic and Panharmonic Functions
The m-dimensional modified Helmholtz equation is considered and two relations between its solutions (called panharmonic functions) and harmonic...
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Topological characterizations of recurrence, Poisson stability, and isometric property of flows on surfaces
The long-time behavior is one of the most fundamental properties of dynamical systems. Poincaré studied the Poisson stability to capture the property...
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Introduction to Recurrence Relations
In this chapter we present fundamental concepts and motivating examples of recurrent sequences, and show connections of recurrence relations to...
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Lacunary Recurrent Relations with Gaps of Length Four for the Bernoulli and Euler Polynomials
We obtain lacunary recurrent relations with gaps of length four for the Bernoulli and Euler polynomials and, as a consequence, known and new lacunary...
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Greatest common divisors for polynomials in almost units and applications to linear recurrence sequences
We bound the greatest common divisor of two coprime multivariable polynomials evaluated at algebraic numbers, generalizing work of Levin, and going...