Generating Functions for Jacobi and Laguerre Polynomials

Srivastava, H. M.

doi:10.2307/2036591

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Polynomial1

Bilinear Generating Function1

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1973

2018

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Cited by 8 publications

(6 citation statements)

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“…which, he observes [14], contains most of the results of Brown [2], [3], Carlitz [4], Srivastava [11] and Zeitlin [17]. Niblett's result is (1.4) with w = l,q=r4t and u = r. Other results of this type are collected in [8].…”

Section: Polynomialmentioning

confidence: 83%

Polynomial Expansions

Fields¹,

Ismail²

1975

Mathematics of Computation

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Section: Polynomialmentioning

confidence: 83%

Polynomial Expansions

Fields¹,

Ismail²

1975

Mathematics of Computation

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“…We are going to obtain a second formula based on a theorem from [55]. Let us formulate the corresponding result explicitly in a slightly less general form that suffices for our purposes.…”

Section: )mentioning

confidence: 99%

“…See [55] for a simple proof. We again use the d-orthogonal polynomials Q n (x) from (4.1) as well as the convention η = 1.…”

Section: )mentioning

confidence: 99%

d-Orthogonal Analogs of Classical Orthogonal Polynomials

Horozov¹

2018

SIGMA

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Abstract. Classical orthogonal polynomial systems of Jacobi, Hermite and Laguerre have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a famous theorem by Bochner they are the only systems on the real line with this property. Similar results hold for the discrete orthogonal polynomials. In a recent paper we introduced a natural class of polynomial systems whose members are the eigenfunctions of a differential operator of higher order and which are orthogonal with respect to d measures, rather than one. These polynomial systems, enjoy a number of properties which make them a natural analog of the classical orthogonal polynomials. In the present paper we continue their study. The most important new properties are their hypergeometric representations which allow us to derive their generating functions and in some cases also Mehler-Heine type formulas.

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“…The poynomials P n,λ,µ (x, u) admit the following generating functions which are recorded similar to Srivastava and Singhal [10] as given below.…”

Section: Bilinear Generating Functionmentioning

confidence: 99%