Growth of partial sums of divergent series

Author:
R. P. Boas

Journal:
Math. Comp. **31** (1977), 257-264

MSC:
Primary 65B15

DOI:
https://doi.org/10.1090/S0025-5718-1977-0440862-0

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

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DOI:
https://doi.org/10.1090/S0025-5718-1977-0440862-0

Article copyright:
© Copyright 1977
American Mathematical Society