OFFSET
1,1
COMMENTS
Hans Rademacher conjectured that C_{011}(N) converge to -0.292927573960. This conjecture is false.
Named after the German-American mathematician Hans Adolph Rademacher (1892-1969). - Amiram Eldar, Jun 22 2021
REFERENCES
Hans Rademacher, Topics in Analytic Number Theory, Springer, 1973, p. 302.
LINKS
Andrew V. Sills and Doron Zeilberger, Rademacher's infinite partial fraction conjecture is (almost certainly) false, arXiv:1110.4932v1 [math.NT], 2011.
Andrew V. Sills and Doron Zeilberger, Rademacher's Infinite Partial Fraction Conjecture is (almost certainly) False, Oct 21 2011; Local copy, pdf file only, no active links.
Andrew V. Sills and Doron Zeilberger, HANS (maple package); Local copy.
FORMULA
See above article for an efficient recurrence.
EXAMPLE
For n=1, the coefficient of 1/(q-1) in the partial fraction decomposition of 1/(1-q) is -1, multiplied by 2! this gives -2.
MAPLE
See above link to HANS (maple package).
CROSSREFS
KEYWORD
sign,more
AUTHOR
Shalosh B. Ekhad, May 03 2012
STATUS
approved