New results on the Stieltjes constants: Asymptotic and exact evaluation

AN ASYMPTOTIC FORM FOR THE STIELTJES CONSTANTS γk(a) AND FOR A SUM Sγ(n) APPEARING UNDER THE LI CRITERION

We present several asymptotic analyses for quantities associated with the Riemann and Hurwitz zeta functions. We first determine the leading asymptotic behavior of the Stieltjes constants γk(a). These constants appear in the regular part of the Laurent expansion of the Hurwitz zeta function. We then use asymptotic results for the Laguerre polynomials Ln to investigate a certain sum Sγ(n) involv...

Asymptotic estimates for Stieltjes constants: a probabilistic approach

Interlacing and asymptotic properties of Stieltjes polynomials

Polynomial solutions to the generalized Lamé equation, the Stieltjes polynomials, and the associated Van Vleck polynomials have been studied since the 1830’s, beginning with Lamé in his studies of the Laplace equation on an ellipsoid, and in an ever widening variety of applications since. In this paper we show how the zeros of Stieltjes polynomials are distributed and present two new interlacin...

Superlinearly convergent exact penalty projected structured Hessian updating schemes for constrained nonlinear least squares: asymptotic analysis

We present a structured algorithm for solving constrained nonlinear least squares problems, and establish its local two-step Q-superlinear convergence. The approach is based on an adaptive structured scheme due to Mahdavi-Amiri and Bartels of the exact penalty method of Coleman and Conn for nonlinearly constrained optimization problems. The structured adaptation also makes use of the ideas of N...

Asymptotic Distributions of Estimators of Eigenvalues and Eigenfunctions in Functional Data

Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...