Numbers generated by the reciprocal of
Author:
F. T. Howard
Journal:
Math. Comp. 31 (1977), 581598
MSC:
Primary 10A40; Secondary 05A17
MathSciNet review:
0439741
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Abstract: In this paper we examine the polynomials and the rational numbers defined by means of We prove that the numbers are related to the Stirling numbers and associated Stirling numbers of the second kind, and we show that this relationship appears to be a logical extension of a similar relationship involving Bernoulli and Stirling numbers. Other similarities between and the Bernoulli numbers are pointed out. We also reexamine and extend previous results concerning and . In particular, it has been conjectured that has the same sign as , where is the zero of with smallest absolute value. We verify this for and show that if the conjecture is not true for , then . We also show that has no integer roots, and in the interval , has either two or three real roots.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197704397414
PII:
S 00255718(1977)04397414
Keywords:
Bernoulli number and polynomial,
Stirling numbers of the second kind,
associated Stirling numbers of the second kind,
Eisenstein's irreducibility criterion,
set partition,
composition,
StaudtClausen theorem
Article copyright:
© Copyright 1977
American Mathematical Society
