We obtain a representation formula for the trigonometric sum f (m, n) and deduce from it the upper bound f(m, n) < (4/p 2 ) m log m+ (4/p 2 )(c -log(p/2)+2C G ) m+O(m/`log m), where C G is the supremum of the function G(t) :=; . k=1 log |2 sin pkt|/(4k 2 -1), over the set of irrationals. The coeffi
An asymptotic formula for the potential of a short cylinder
β Scribed by I.A. Chegis
- Publisher
- Elsevier Science
- Year
- 1985
- Weight
- 545 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0041-5553
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π SIMILAR VOLUMES
The present article is really a continuation of the author's earlier paper [,l] on this subject. The line of investigation described previously is rounded off by deriving some further numcrical results, which include, in particular, an asymptotic fonnula for the number of complete propositional conn
In this paper it is shown that for every fixed k 1> 3, G(n; d = k) = 2(~) (6.2 -k + o(1))", where G(n; d = k) denotes the number of graphs of order n and diameter equal to k. It is also proved that for every fixed k>~2, lim,~G(n;d=k)/G(n;d=k+ 1)=lim.o~G(n;d=n-k)/ G(n;d=n-k+ 1)= oo hold.
The arithmetic function r & k (n) counts the number of ways to write a natural number n as the difference of two kth powers (k 2 fixed). The investigation of the asymptotic behaviour of the Dirichlet summatory function of r & k (n) leads in a natural way to a certain error term 2 & k (t). In this ar