Related papers: Some inversion formulas and formulas for Stirling …
In the paper, the author derives several "diagonal" recurrence relations, constructs some inequalities, finds monotonicity, and poses a conjecture related to Stirling numbers of the second kind.
This paper proves why the Stirling numbers show up in a experimentally determined formula for the $k$-bonaccis. We develop a bijection between a previously determined summation formula for $k$-bonaccis and an experimentally determined…
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…
Several new estimates for the 2-adic valuations of Stirling numbers of the second kind are proved. These estimates, together with criteria for when they are sharp, lead to improvements in several known theorems and their proofs, as well as…
In an earlier paper, we defined and studied q-analogues of the Stirling numbers of both types for the Coxeter group of type B. In the present work, we show how this approach can be extended to all irreducible complex reflection groups G.…
The objective of this paper is, in the main, twofold: Firstly, to develop an algebraic setting for dealing with Bell polynomials and related extensions. Secondly, based on the author's previous work on multivariate Stirling polynomials…
We consider general formulations of the change of variable formula for the Riemann-Stieltjes integral, including the case when the substitution is not invertible.
A permutation $\sigma$ of a multiset is called Stirling permutation if $\sigma(s)\ge \sigma(i)$ as soon as $\sigma(i)=\sigma(j)$ and $i<s<j.$ In our paper we study Stirling polynomials that arise in the generating function for descent…
A family of original formulae for computing number PI and its proof are presented. An algorithm is proposed to validate the results of this new algorithm.
In this note, we present several identities involving binomial coefficients and the two kind of Stirling numbers.
A review of the inverse scattering transform is given, and an introduction to solitons is provided.
A number of identities are proved by using Stirling transforms. These identities involve Stirling numbers of the first and second kinds, hyperharmonic and derangement numbers, Bernoulli and Euler numbers and polynomials, powers, power sums,…
Two new approaches to numerical QFT are presented.
We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
This paper proves a reciprocity formula for modular inverses for non-zero integers and demonstrates some applications of the reciprocity formula in calculating or verifying some modular inverses of specific forms, including the modular…
Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers…
We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…
Inversion sequences, also known as subexcedant sequences, form a fundamental class of objects in enumerative combinatorics. In this paper, we study the joint distribution of five statistics on inversion sequences. While several statistics…
In this paper, we present a new approach to the convolved Fibonacci numbers arising from the generating function of them and give some new and explicit identities for the convolved Fibonacci numbers.