Various applications of the (exponential) complete Bell polynomials

Abstract

In a rather straightforward manner, we develop the well-known formula for the Stirling numbers of the first kind in terms of the (exponential) complete Bell polynomials where the arguments include the generalised harmonic numbers. We also show how the (exponential) complete Bell polynomials feature in a number of other areas of mathematical interest.

Contains a correction to section 6

References in corpus (3)

• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I
• A Set of Identities for a Class of Alternating Binomial Sums Arising in Computing Applications
• Some integrals involving the Stieltjes constants

Cited by in corpus (5)

• On an integral involving the digamma function
• Some possible approaches to the Riemann Hypothesis via the Li/Keiper constants
• Determination of the Stieltjes constants at rational arguments
• Particular solutions of the inverse problem for 1D Vlasov-Maxwell equilibria using Hermite polynomials
• Some relations involving the higher derivatives of the Riemann zeta function