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1972
Publisher Summary This chapter presents the theory of recurrence relations. The tower of Hanoi puzzle, for example, involved the recurrence relation Sn+1 = 2Sn + 1. In this situation, the recurrence relation related the minimum number of moves required to transfer a tower of n + 1 rings in the puzzle to the minimum number of moves required to transfer
K.D. Fryer, Gerald Berman
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Publisher Summary This chapter presents the theory of recurrence relations. The tower of Hanoi puzzle, for example, involved the recurrence relation Sn+1 = 2Sn + 1. In this situation, the recurrence relation related the minimum number of moves required to transfer a tower of n + 1 rings in the puzzle to the minimum number of moves required to transfer
K.D. Fryer, Gerald Berman
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Probabilistic Recurrence Relations [PDF]
, 2010 A sampling of discrete probability problems, some of them coming from consulting work, is presented. We demonstrate how a probabilistic recurrence relation arises from the pit of the problem and present ways and means of solving the recurrence relation.
S. Kasala +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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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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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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2013
Walter Gautschi is a giant in the field of linear recurrence relations. His concern is with stability in computing solutions \( \{y_{n}\}_{n=0}^{\infty} \) of such equations. Suppose the recurrence relation is of the form $$\displaystyle{ y_{n+1} + a_{n}y_{n} + b_{n}y_{n-1} = 0\qquad \mbox{ for}\quad n = 1,2,3,\ldots.}$$ (21.1) It seems so ...
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Walter Gautschi is a giant in the field of linear recurrence relations. His concern is with stability in computing solutions \( \{y_{n}\}_{n=0}^{\infty} \) of such equations. Suppose the recurrence relation is of the form $$\displaystyle{ y_{n+1} + a_{n}y_{n} + b_{n}y_{n-1} = 0\qquad \mbox{ for}\quad n = 1,2,3,\ldots.}$$ (21.1) It seems so ...
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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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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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Drug-related recurrent meningitis
Journal of Infection, 1988A 56-year-old man presented with recurrent smear and culture-negative meningitis having ingested Ibuprofen before each episode. The association between Ibuprofen and meningitis has been well established in systemic lupus erythematosus but has been reported only rarely in previously healthy patients.
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