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SUMMARY:Cormac O'Sullivan (Bronx Community College (CUNY))
DTSTART:20230525T193000Z
DTEND:20230525T195500Z
DTSTAMP:20260423T041812Z
UID:CANT2023/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2023/47/
 ">A hidden link between two of Ramanujan’s approximations</a>\nby Cormac
  O'Sullivan (Bronx Community College (CUNY)) as part of Combinatorial and 
 additive number theory (CANT 2023)\n\nLecture held in Room 4102 in CUNY Gr
 ad Center.\n\nAbstract\nIn consecutive notebook entries\, Ramanujan gave a
 symptotic approximations to the exponential function and the exponential i
 ntegral. The asymptotic expansion coefficients seem to agree up to an alte
 rnating sign\, as we conjectured in an earlier paper. We establish this hi
 dden link with a combinatorial proof that involves Stirling numbers\, seco
 nd-order Eulerian numbers\, modifications of both of these\, and Stirling'
 s approximation to the gamma function. An analytic second proof has also b
 een provided by a referee. It is not yet clear if this result is an oddity
  or part of a broader picture.\n
LOCATION:https://researchseminars.org/talk/CANT2023/47/
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