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Fourth-order difference equation for the first associated of classical discrete orthogonal polynomials

✍ Scribed by A. Ronveaux; E. Godoy; A. Zarzo; I. Area

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
245 KB
Volume
90
Category
Article
ISSN
0377-0427

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πŸ“œ SIMILAR VOLUMES

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We derive the fourth-order difference equation satisfied by the associated order r of classical orthogonal polynomials of a discrete variable. The coefficients of this equation are given in terms of the polynomials a and z which appear in the discrete Pearson equation A(ap)= zp defining the weight

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We derive the fourth-order q-difference equation satisfied by the first associated of the q-classical orthogonal polynomials. The coefficients of this equation are given in terms of the polynomials tr and z which appear in the q-Pearson difference equation Dq(tr p)= zp defining the weight p of the q

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Three equivalent forms of the fourth-order difference equation obeyed by the associated Meixner polynomials (with a nonnegative real association parameter) are derived from a refinement of a recent result due to .

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Starting from the DΟ‰-Riccati difference equation satisfied by the Stieltjes function of a linear functional, we work out an algorithm which enables us to write the general fourthorder difference equation satisfied by the associated of any integer order of orthogonal polynomials of the βˆ†-Laguerre-Hah