DeepAI AI Chat
Log In Sign Up

Inversion formula with hypergeometric polynomials and its application to an integral equation

by   Ridha Nasri, et al.

For any complex parameters x and ν, we provide a new class of linear inversion formulas T = A(x,ν) · S S = B(x,ν) · T between sequences S = (S_n)_n ∈N^* and T = (T_n)_n ∈N^*, where the infinite lower-triangular matrix A(x,ν) and its inverse B(x,ν) involve Hypergeometric polynomials F(·), namely { < a r r a y > . for 1 ≤ k ≤ n. Functional relations between the ordinary (resp. exponential) generating functions of the related sequences S and T are also given. These new inversion formulas have been initially motivated by the resolution of an integral equation recently appeared in the field of Queuing Theory; we apply them to the full resolution of this integral equation. Finally, matrices involving generalized Laguerre polynomials polynomials are discussed as specific cases of our general inversion scheme.


page 1

page 2

page 3

page 4


An inversion formula with hypergeometric polynomials and application to singular integral operators

Given parameters x ∉R^- ∪{1} and ν, Re(ν) < 0, and the space H_0 of enti...

Complementary Romanovski-Routh polynomials and their zeros

The efficacy of numerical methods like integral estimates via Gaussian q...

On the inversion of the Laplace transform (In Memory of Dimitris Gatzouras)

The Laplace transform is a useful and powerful analytic tool with applic...

Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems

Data-driven reduced order models (ROMs) are combined with the Lippmann-S...

On 120-avoiding inversion and ascent sequences

Recently, Yan and the first named author investigated systematically the...

Improved Laguerre Spectral Methods with Less Round-off Errors and Better Stability

Laguerre polynomials are orthogonal polynomials defined on positive half...