Asymptotic formulae for linear equations
نویسندگان
چکیده
منابع مشابه
Asymptotic Constancy in Linear Difference Equations: Limit Formulae and Sharp Conditions
It is found that every solution of a system of linear delay difference equations has finite limit at infinity, if some conditions are satisfied. These are much weaker than the known sufficient conditions for asymptotic constancy of the solutions. When we impose some positivity assumptions on the coefficient matrices, our conditions are also necessary. The novelty of our results is illustrated b...
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Let ts,n be the n-th positive integer number which can be written as a power p, t ≥ s, of a prime p (s ≥ 1 is fixed). Let πs(x) denote the number of prime powers p, t ≥ s, not exceeding x. We study the asymptotic behaviour of the sequence ts,n and of the function πs(x). We prove that the sequence ts,n has an asymptotic expansion comparable to that of pn (the Cipolla’s expansion).
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1972
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500001579