Growth of partial sums of divergent series
Author:
R. P. Boas
Journal:
Math. Comp. 31 (1977), 257264
MSC:
Primary 65B15
MathSciNet review:
0440862
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Abstract: Let be a divergent series of decreasing positive terms, with partial sums , where f decreases sufficiently smoothly; let and let be the inverse of . Let be the smallest integer n such that but ; let be the analog of Euler's constant; let . Call a Comtet function for if when the fractional part of is less than and when the fractional part of is greater than . It has been conjectured that is a Comtet function for . It is shown that in general there is a Comtet function of the form For there is a Comtet function of the form . Some numerical results are presented.
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 G. H. HARDY, Orders of In finitv. 2nd ed., Cambridge Univ. Press, New York, 1924.
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 K. A. KARPOV & S. N. RAZUMOVSKIĬ, Tablicy Integral'nogo Logarifma, Izdat. Akad. Nauk SSSR, Moscow, 1956, 319 pp. MR 19, 67; erratum, ibid., p. 1431. MR 0085623 (19:67h)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197704408620
PII:
S 00255718(1977)04408620
Article copyright:
© Copyright 1977
American Mathematical Society
