منابع مشابه
Apery Sequences and Legendre Transforms
A lower bound for the minimal length of the polynomial recurrence of a binomial sum is obtained. 2000 Mathematics subject classification: primary 11B37. A sequence an satisfies a polynomial recurrence of length r and degree m if there exist r polynomials Po, Pu ... , Pr_u with degree at most m such that (1) Po(n)an + P x { n ) a n ^ + ••• + P r ^ ( n ) a n r = 0 for n > r. For a sequence an the...
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is obtained by applying successive integration by parts to the integral represented by the left-hand member of this equation so that the new integrand is the product of F by [(1 —x2)P„' ]', and by replacing this second factor by — n(n + l)Pn according to Legendre's differential equation [l]. Thus certain boundary value problems in ordinary and partial differential equations that involve the dif...
متن کاملToeplitz transforms of Fibonacci sequences
We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.
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Two families of binary sequences are constructed from dth order cyclotomic generator and from dth order generalized cyclotomic generator with respect to two distinct primes respectively. By using estimates of certain exponential sums over rings or fields, the upper bounds of both the well-distribution measure and the order k (at least for small k) correlation measure of the resulting binary seq...
متن کاملtoeplitz transforms of fibonacci sequences
we introduce a matricial toeplitz transform and prove that the toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. we investigate the injectivity of this transform and show how this distinguishes the fibonacci sequence among other recurrence sequences. we then obtain new fibonacci identities as an application of our transform.
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1995
ISSN: 0263-6115
DOI: 10.1017/s1446788700038350