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High-order recurrence relations, Hermite-Padé approximation and Nikishin systems
, 2016The study of sequences of polynomials satisfying high-order recurrence relations is connected with the asymptotic behaviour of multiple orthogonal polynomials, the convergence properties of type II Hermite-Padé approximation and eigenvalue distribution ...
D. B. Rolan'ia +2 more
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Introduction to Recurrence Relations
2020In this chapter we present fundamental concepts and motivating examples of recurrent sequences, and show connections of recurrence relations to mathematical modeling, algebra, combinatorics, and analysis. There are numerous sources presenting the classical theory.
Ovidiu Bagdasar, Dorin Andrica
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On the limit of a recurrence relation
Journal of Difference Equations and Applications, 1999In this paper we study the asymptotic properties of the sequence of integers g(n), defined by the following recurrence relation: where ∞>0 and [x] denotes the largest not greater than x. For any ∞>0, the limit g(n)/n ∞ exists. We prove that for ∞=2, this limit is always rational.
Ron Graham, Catherine H. Yan
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Factors in recurrence relations
The Mathematical Gazette, 1989Suppose we are given a sequence of numbers defined by a linear recurrence relation with constant coefficients, for example the Fibonacci numbers which are defined by:
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1971
Publisher Summary The method of reducing a problem to an analogous problem involving a smaller number of objects is called the method of recurrence relations. With the help of a recurrence relation, a problem involving n objects to one involving n – 1 objects, then to one involving n – 2 objects, and so on, can be reduced.
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Publisher Summary The method of reducing a problem to an analogous problem involving a smaller number of objects is called the method of recurrence relations. With the help of a recurrence relation, a problem involving n objects to one involving n – 1 objects, then to one involving n – 2 objects, and so on, can be reduced.
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Recurrence relations for the Cartesian derivatives of the Zernike polynomials.
Journal of The Optical Society of America A-optics Image Science and Vision, 2014A recurrence relation for the first-order Cartesian derivatives of the Zernike polynomials is derived. This relation is used with the Clenshaw method to determine an efficient method for calculating the derivatives of any linear series of Zernike ...
Philip Stephenson
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Bounds, Asymptotic Behavior and Recurrence Relations for the Jacobi-Dunkl Polynomials
, 2014In this paper, we establish explicit formulas and recurrence relations for the Jacobi-Dunkl polynomials. Bounds and asymptotic behavior of these polynomials are also given.
F. Chouchene
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Recurrence Relations for Powers
1979Publisher Summary This chapter explains the recurrence relations for powers. It presents the solution of equations of the form xp = N, where N is a given number, 0 < N < 1, and p is a real number, ½, ⅓, −1, for instance. The chapter discusses various sequences {xn} whose limit is the solution and whose terms are defined by recurrence relations ...
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Mathematical Proceedings of the Cambridge Philosophical Society, 1968
Slater ((5), p. 27) and Bose ((1), p. 202) have obtained certain recurrence relations about Whittaker and hypergeometric functions. In this note an attempt has been made to obtain generalizations of these recurrence relations.
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Slater ((5), p. 27) and Bose ((1), p. 202) have obtained certain recurrence relations about Whittaker and hypergeometric functions. In this note an attempt has been made to obtain generalizations of these recurrence relations.
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