Journal of Integer Sequences, Vol. 23 (2020), Article 20.11.7

New Series Identities with Cauchy, Stirling, and Harmonic Numbers, and Laguerre Polynomials

Khristo N. Boyadzhiev
Department of Mathematics
Ohio Northern University
Ada, Ohio 45810


We use an interplay between Newton series and binomial formulas to generate a number of series identities involving Cauchy numbers (also known as Gregory coefficients or Bernoulli numbers of the second kind), harmonic numbers, Laguerre polynomials, and Stirling numbers of the first kind.

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(Concerned with sequences A000108 A006232 A006233 A008275 A048994.)

Received November 8 2019; revised versions received April 6 2020; October 19 2020; December 5 2020. Published in Journal of Integer Sequences, December 6 2020.

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