Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606973 | Journal of Approximation Theory | 2015 | 17 Pages |
Abstract
We study solutions (xn)n∈N(xn)n∈N of nonhomogeneous nonlinear second order difference equations of the typeℓn=xn(σn,1xn+1+σn,0xn+σn,−1xn−1)+κnxn,n∈N,with given initial data {x0∈R&x1∈R+} where (ℓn)n∈N∈R+&(σn,0)n∈N∈R+&(κn)n∈N∈R, and the left and right σσ-coefficients satisfy either (σn,1)n∈N∈R+&(σn,−1)n∈N∈R+ or (σn,1)n∈N∈R0+&(σn,−1)n∈N∈R0+. Depending on one’s standpoint, such equations originate either from orthogonal polynomials associated with certain Shohat-Freud-type exponential weight functions or from Painlevé’s discrete equation #1, that is, .
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Saud M. Alsulami, Paul Nevai, József Szabados, Walter Van Assche,