Related papers: Peakons and Cauchy Biorthogonal Polynomials

Preliminary version of Chapter 2 in the book "Encyclopedia of Special functions: The Askey-Bateman Project, Vol. 2: Multivariate special functions", T. H. Koornwinder and J. V. Stokman (eds.), Cambridge University Press, 2021.

This paper provides a finite pair of biorthogonal matrix polynomials and their finite biorthogonality, several recurrence relations, matrix differential equation, generating function and integral representation.

This paper is superseded by arXiv:1106.3363.

This paper has been withdrawn by the authors because it has been merged with paper arXiv:0903.3501v1 [math.DG]

Recently, degenerate Cauchy numbers and polynomials are introduced in [10]. In this paper, we study the degenerate Cauchy numbers and polynomials which are different from the previous degenerate Cauchy numbers and polynomials. In addition,…

In this paper, we study higher-order Cauchy of the first kind and poly-Cauchy of the first kind mixed type polynomials with viewpoint of umbral calculus and give some interesting identities and formulae of those polynomials which are…

These supplementary notes in the ArXiv are a companion to our paper "Bocher contractions of conformally superintegrable Laplace equations" [arXiv:1512.09315]. They contain background material and the details of the extensive computations…

In this paper, we consider the poly-cauchy polynomials and numbers of the second kind which were studied by Komatsu in [10]. We note that the poly-Cauchy polynomials of the second kind are the special generalized Bernoulli polynomials of…

The contents are divided into two papers "The Monotone Cumulants" (arXiv:0907.4896) and "Conditionally monotone independence" (arXiv:0907.5473).

%auto-ignore The paper has been withdrawn by authors. The completely revised version can be found under the following preprint-no: hep-ph/9910282.

In this paper, we investigate some properties of higher-order Cauchy of the second kind and poly-Cauchy of the second mixed type polynomials with umbral calculus viewpoint. From our investigation, we derive many interesting identities of…

The content of this paper is now available as part of arXiv:0802.2019

This paper is a revised version of a previously posted paper in arxiv. The authors posted it as a new submission by mistake. The latest version of the paper can be found at arXiv:math-ph/0512003v2

In this paper, we consider Poisson-Charlier and poly-Cauchy mixed type polynomials and give various identities of those polynomials which are derived from umbral calculus.

Comment on ``Gibbs Sampling, Exponential Families, and Orthogonal Polynomials'' [arXiv:0808.3852]

We give historical remarks related to arXiv:2112.14547 ("A New Method of Construction of Permutation Trinomials with Coefficients 1", by Guo et al.). In particular, we show that the "new" permutation polynomials in that paper are actually…

Comment on ``Gibbs Sampling, Exponential Families and Orthogonal Polynomials'' [arXiv:0808.3852]

This manuscript, a revised version of arXiv:0811.3168v1, was inadvertently submitted as a separate paper. It can now be accessed, including some final corrections for the published version, as arXiv:0811.3168v2.

This paper is now part of the new paper "Series with Hermite polynomials and applications" arXiv:1710.00687.

The paper investigates the properties of certain biorthogonal polynomials appearing in a specific simultaneous Hermite-Pade' approximation scheme. Associated to any totally positive kernel and a pair of positive measures on the positive…