Connection problems via lowering operators

Cheikh, Youssèf Ben; Chaggara, Hamza

doi:10.1016/j.cam.2004.02.024

Cited by 30 publications

(23 citation statements)

References 15 publications

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“…LEMMA 2.3 (see [3], Corollary 3.9) Let fP n g n!0 and fQ n g n!0 be two polynomial sets of Boas-Buck type that are generated, respectively, by are given by…”

Section: The Methodsmentioning

confidence: 99%

“…Let us mention that Corollary 3.1 was already given in [3] and applied essentially to some q-polynomial sets. Next, we consider some examples.…”

Section: The Methodsmentioning

confidence: 99%

“…A general method, based on lowering operators and generating functions, was developed in [2,3] to solve connection and linearization problems [4,7]. The purpose of this work is to use this approach to express explicitly the coefficients C m ðn, aÞ.…”

Section: Introductionmentioning

confidence: 99%

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Duplication coefficients via generating functions

Chaggara

Koepf

2007

Complex Variables and Elliptic Equations

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In this article, we solve the duplication problem,where fP n g n!0 belongs to a wide class of polynomials, including the classical orthogonal polynomials (Hermite, Laguerre, Jacobi) as well as the classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouk) for the specific case a ¼ À1. We give closed-form expressions as well as recurrence relations satisfied by the duplication coefficients.

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“…LEMMA 2.3 (see [3], Corollary 3.9) Let fP n g n!0 and fQ n g n!0 be two polynomial sets of Boas-Buck type that are generated, respectively, by are given by…”

Section: The Methodsmentioning

confidence: 99%

“…Let us mention that Corollary 3.1 was already given in [3] and applied essentially to some q-polynomial sets. Next, we consider some examples.…”

Section: The Methodsmentioning

confidence: 99%

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Duplication coefficients via generating functions

Chaggara

Koepf

2007

Complex Variables and Elliptic Equations

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“…Afterward, Da-Qian Lu found differential equations for generalized Bernoulli polynomials in [7]. Recently, several interesting properties and relationships involving the classical Appell type polynomials were investigated [5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Difference equations of q-Appell polynomials

Mahmudov

2014

Applied Mathematics and Computation

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Keywords: q-Appell polynomials Lowering operators q-Bernoulli polynomials q-Euler polynomials q-Genocchi polynomials q-Hermite polynomials a b s t r a c tIn this paper, we study some properties of the q-Appell polynomials, including the recurrence relations and the q-difference equations which extend some known classical (q ¼ 1) results. We also provide the recurrence relations and the q-difference equations for q-Bernoulli polynomials, q-Euler polynomials, q-Genocchi polynomials and for q-Hermite polynomials, as special cases of q-Appell polynomials.

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“…A recurrent approach called navima-algorithm which consists a method in computing C m (n) as solution of a recurrence relation can also be applied to solve connection and linearization problems (see, for instance, [19][20][21][22][23][24][25]). A general method which does not need particular properties of the polynomials involved in the problem based on the corresponding lowering operators and dual sequences [1] was developed in [3] to express explicitly the connection coefficients between two given polynomial sets.…”

Section: Introductionmentioning

confidence: 99%