In this paper, we trace back the genesis of Aitken's Δ 2 process and Shanks' sequence
transformation. These methods, which are extrapolation methods, are used for accelerating …

Skew-orthogonal polynomials (SOPs) arise in the study of the n-point distribution function for
orthogonal and symplectic random matrix ensembles. Motivated by the average of …

We show that the Wynn recurrence (the missing identity of Frobenius of the Padé
approximation theory) can be incorporated into the theory of integrable systems as a …

We show that solution to the Hermite–Padé type I approximation problem leads in a natural
way to a subclass of solutions of the Hirota (discrete Kadomtsev–Petviashvili) system and of …

The relationship between matrix integrals and integrable systems was revealed more than
20 years ago. As is known, matrix integrals over a Gaussian ensemble used in random …

In this paper, we propose a generalized discrete Lotka-Volterra equation and explore its
connections with symmetric orthogonal polynomials, Hankel determinants and convergence …

We construct new sequence transformations based on Wynn's epsilon and rho algorithms.
The recursions of the new algorithms include the recursions of Wynn's epsilon and rho …

Inspired by the connection between the Dodgson's condensation algorithm and Hirota's
difference equation, we consider condensation algorithms for Pfaffians from the perspectives …

There are two objectives for this paper. Firstly, we shall introduce the Thukral-determinantal
formula, and secondly, we shall demonstrate the similarities between the well-established …

Firstly, a new sequence transformation that can be expressed in terms of a ratio of two
pfaffians is derived based on a special kernel. It can be regarded as a direct generalization …