A very slowly convergent sequence of continuous functions
نویسندگان
چکیده
منابع مشابه
Very Slowly Varying Functions
A real-valued function f of a real variable is said to be (p-slowly varying ((p-s .v.) if limn_ . rp (x) [ f (x + a) f (x)] = 0 for each a. It is said to be uniformly 9-slowly varying (u . (P-s .v .) if limn-. . sup, e r rp(x) ; f (x-a) f (x)I =0 for every bounded interval I. It is supposed throughout that rp is positive and increasing . It is proved that if w increases rapidly enough, then eve...
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The harmonic series diverges. But if we delete from it all terms whose denominators contain any string of digits such as “9”, “42”, or “314159”, then the sum of the remaining terms converges. These series converge far too slowly to compute their sums directly. We describe an algorithm to compute these and related sums to high precision. For example, the sum of the series whose denominators cont...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0315324-x