Related papers: Using the Jacobi-Trudi formula to compute Stirling…
We present new determinant expressions for regularized Schur multiple zeta values. These generalize the known Jacobi-Trudi formulae and can be used to quickly evaluate certain types of Schur multiple zeta values. Using these formulae we…
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.
We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…
Using numerical, theoretical and general methods, we construct evaluation formulas for the Jacobi $\theta$ functions. Some of our results are conjectures, but are verified numerically.
Jacobi sums and cyclotomic numbers are the important objects in number theory. The determination of all the Jacobi sums and cyclotomic numbers of order $e$ are merely intricate to compute. This paper presents the lesser numbers of Jacobi…
We investigate the diagonal generating function of the Jacobi-Stirling numbers of the second kind $ \JS(n+k,n;z)$ by generalizing the analogous results for the Stirling and Legendre-Stirling numbers. More precisely, letting…
Jacobi-Trudy formula for a generalisation of Schur polynomials related to any sequence of orthogonal polynomials in one variable is given. As a corollary we have Giambelli formula for generalised Schur polynomials.
Rational solutions for a $q$-difference analogue of the Painlev\'e III equation are considered. A Determinant formula of Jacobi-Trudi type for the solutions is constructed.
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.
In the paper, the author finds an explicit formula for computing Bell numbers in terms of Kummer confluent hypergeometric functions and Stirling numbers of the second kind.
In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
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 the following short paper we list some useful results concerning determinants and inverses of matrices. First we show, how to calculate determinants of $d \times d$ matrices, if their traces are known. As a next step $4 \times 4$…
Associated to each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention,…
We present a survey on recent results about Stirling's formula. More exactly, we reffer to a method using a form of Cesaro-Stolz lemma firstly introduced in [C. Mortici Product approximations via asymptotic integration Amer. Math. Monthly…
We present an improved form of the algorithm for constructing Jacobi rotations. This is simultaneously a more accurate code for finding the eigenvalues and eigenvectors of a real symmetric 2x2 matrix.
We give some formulas of poly-Cauchy numbers by the $r$-Stirling transform. In the case of the classical or poly-Bernoulli numbers, the formulas are with Stirling numbers of the first kind. In our case of the classical or poly-Cauchy…
In this paper, we use our previous study of the higher order Bernoulli numbers $B_n^{(l)}$ to investigate the $p$-adic properties of the Stirling numbers of the second kind $S(n,k)$. For example, we give a new, greatly simplified proof of…
This article evaluates the determinants of two classes of special matrices, which are both from a number theory problem. Applications of the evaluated determinants can be found in [arXiv:math.NT/0509523]. Note that the two determinants are…