Inversion, Multiplication and Connection Formulae of Classical Continuous Orthogonal Polynomials

Tcheutia, Daniel Duviol

doi:10.1007/978-3-030-36744-2_5

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2024

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“…Proof. For the q-Laguerre polynomials, the connection formula [13], [22] L (α) n (x; q) = n m=0 (q; q) n q m+β+1…”

Section: Expansion Of Thementioning

confidence: 99%

Recurrence relation approach for expansion and connection coefficients in series of q-Laguerre polynomials

Tcheutia,

Mboutngam,

Foupouagnigni

2024

Preprint

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In this manuscript, we expand some functions of a q-discrete variable as linear combination of the q-Laguerre polynomials. The recurrence relations satisfied by the expansion coefficients are derived and in many cases, explicit solutions of these recurrence relations are computed. We show how our results can be used to solve some q-difference equations and to illustrate this, we solve the connection problem between classical q-orthogonal polynomials and the q-Laguerre polynomials. Mathematics Subject Classification (2010). 33D45, 42C10, 65Q30.

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“…Proof. For the q-Laguerre polynomials, the connection formula [13], [22] L (α) n (x; q) = n m=0 (q; q) n q m+β+1…”

Section: Expansion Of Thementioning

confidence: 99%

Recurrence relation approach for expansion and connection coefficients in series of q-Laguerre polynomials

Tcheutia,

Mboutngam,

Foupouagnigni

2024

Preprint

View full text Add to dashboard Cite

show abstract

Inversion, Multiplication and Connection Formulae of Classical Continuous Orthogonal Polynomials

Cited by 1 publication

References 17 publications

Recurrence relation approach for expansion and connection coefficients in series of q-Laguerre polynomials

Recurrence relation approach for expansion and connection coefficients in series of q-Laguerre polynomials

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