Related papers: Some inversion formulas and formulas for Stirling …

A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.

Some new integrals involving the Stieltjes constants are developed in this paper.

We study inverse factorial series and their relation to Stirling numbers of the first kind. We prove a special representation of the polylogarithm function in terms of series with such numbers. Using various identities for Stirling numbers…

In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the first kind. As by-products, the author also recovers three explicit formulas for special values of the Bell polynomials of the second kind.

In this paper, algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a two-term recurrence. We derive a general identity which…

We introduce a new sequence of unsigned degenerate Stirling numbers of the first kind. Following the work of Adell-Lekuona, who represented unsigned Stirling numbers of the first kind as multiples of the expectations of specific random…

By means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial…

We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.

In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

In this note, we derive an alternative recursive formula for the sums of powers of integers involving the Stirling numbers of the first kind. As a remarkable by-product, we provide a non-recursive definition of the Catalan numbers.

In this paper, we count a dual set of Stirling permutations by the number of alternating runs. Properties of the generating functions, including recurrence relations, grammatical interpretations and convolution formulas are studied.

This paper gives new explicit formulas for sums of powers of integers and their reciprocals.

The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.

We give explicit expressions for higher order convolutions of Cauchy numbers, either as one single integral or in terms of the Stirling numbers of the first and second kinds.

Some new integrals involving the Stieltjes constants are developed in this paper.

In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several…

In the paper, the authors establish an explicit formula for computing Bernoulli polynomials at non-negative integer points in terms of $r$-Stirling numbers of the second kind.

We present new proofs for some summation identities involving Stirling numbers of both first and second kind. The two main identities show a connection between Stirling numbers and Bessel numbers. Our method is based on solving a particular…

In this paper, we consider a generalization of the Stirling number sequence of both kinds by using a specialization of a new family of symmetric functions. We give combinatorial interpretations for this symmetric functions by means of…