Exact expansions of Hankel transforms and related integrals

Hankel hyperdeterminants and Selberg integrals

Abstract. We investigate the simplest class of hyperdeterminants defined by Cayley in the case of Hankel hypermatrices (tensors of the form Ai1i2...ik = f(i1+i2+· · ·+ik)). It is found that many classical properties of Hankel determinants can be generalized, and a connection with Selberg type integrals is established. In particular, Selberg’s original formula amounts to the evaluation of all Ha...

Fast Hankel Transforms

JOHANSEN, H. K., and SORENSEN, K., 1979, Fast Hankel Transforms, Geophysical Prospecting 27, 876-901. Inspired by the linear filter method introduced by D. P. Ghosh in rg7o we have developed a general theory for numerical evaluation of integrals of the Hankel type: m g(r) = Sf(A)hJ,(Ar)dh; v > I. II Replacing the usual sine interpolating function by sinsh (x) = a . sin (xx)/sinh (UTW), where th...

Hankel matrix transforms and operators

Correspondence: homidan@kfupm. edu.sa Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, P. O. Box 119, Saudi Arabia Abstract Hankel operators and Hankel transforms are required in a number of applications. This article proves a number of theorems that efficiently and accurately approximates a function using Hankel transforms and Hankel sum....

Selberg integrals and Catalan-Pfaffian Hankel determinants

In our previous works “Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants” (by M.Ishikawa, H. Tagawa and J. Zeng, J. Combin. Theory Ser. A, 120, 2013, 1263–1284) we have proposed several ways to evaluate certain Catalan-Hankel Pffafians and also formulated several conjectures. In this work we propose a new approach to compute these Catalan-Hankel Pffafians using Sel...

Asymptotic Expansions for Integrals