Orthogonal polynomials and continued fractions arising from contiguous relations and generalizations of Kummer and q-Kummer identities

In this paper, we show formally how can we generate continued fractions starting from three-term contiguous relations. Then as examples, starting from certain contiguous relations for 2 F 1 and 2 ϕ 1 , we derive orthogonal polynomials, continued fractions and in case of 2 F 1 , the measure of orthog...

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Vydáno v:The Ramanujan journal Ročník 49; číslo 2; s. 353 - 369
Hlavní autor: Mansour, Zeinab S. I.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 15.06.2019
Springer Nature B.V
Témata:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Orthogonality
Polynomials
Hypergeometric and basic hypergeometric functions
39A10
39A13
Orthogonal polynomials
30B70
Contiguous relations
Continued fractions
33C05
33D15
ISSN:1382-4090, 1572-9303
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Shrnutí:In this paper, we show formally how can we generate continued fractions starting from three-term contiguous relations. Then as examples, starting from certain contiguous relations for 2 F 1 and 2 ϕ 1 , we derive orthogonal polynomials, continued fractions and in case of 2 F 1 , the measure of orthogonality. Also, a generalization of q -Kummer’s identity is introduced.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-018-0015-x