Connection problems via lowering operators

Journal of Computational and Applied Mathematics

Volumn 178, Issue 1-2 SPEC. ISS., 2005, Pages 45-61

  Ben Cheikh, Y ^a   Chaggara, H ^b  

^a FACULTÉ DES SCIENCES DE MONASTIR   (Tunisia)

^b UNIVERSITY OF MONASTIR   (Tunisia)

Author keywords

Appell polynomials; Addition formula; Boas Buck polynomials; Connection coefficients; Duplication formula; Lowering operators

Indexed keywords

ALGORITHMS; CONVOLUTION; MATHEMATICAL OPERATORS; SET THEORY; THEOREM PROVING;

ADDITION FORMULA; APPELL POLYNOMIALS; BOAS-BUCK POLYNOMIALS; CONNECTION COEFFICIENTS; DUPLICATION FORMULA; LOWERING OPERATOR; POLYNOMIAL SET;

POLYNOMIALS;

EID: 14844359730     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.02.024     Document Type: Article

References (25)

1. M. Abramowitz I.A. Stegun Handbook of Mathematical Functions 1964 National Bureau of Standards Washington, DC
2. I. Area E. Godoy A. Ronveaux A. Zarzo Solving connection and linearization problems within the Askey scheme and its q-analogue via inversion formulas J. Comput. Appl. Math. 133 2001 151-162
3. I. Area E. Godoy A. Ronveaux A. Zarzo Classical discrete orthogonal polynomials, Lah numbers and involutory matrices Appl. Math. Lett. 16 2003 383-387
4. Y. Ben Cheikh On obtaining dual sequences via quasi-monomiality Georgian Math. J. 9 2002 413-422
5. Y. Ben Cheikh Some results on quasi-monomiality Appl. Math. Comput. 141 2003 63-76
6. C. Berg M.E.H. Ismail q -Hermite polynomials and classical orthogonal polynomials Canad. J. Math. 48 1996 43-63
7. R.P. Boas Jr. R.C. Buck Polynomial Expansions of Analytic Functions second ed. 1964 Springer Berlin, Göttingen, Heidelberg
8. L. Carlitz Some multiplication formulas Rend. Semi. Math. Padova 32 1962 239-242
9. T.S. Chihara An Introduction to Orthogonal Polynomials 1978 Gordon and Breach New York, London, Paris
10. A. Erdélyi A. Magnus W. Oberhettinger F.G. Tricomi Higher Transcendental Functions vols. I and II 1953 McGraw-Hill New York, Toronto, London
11. H.W. Gould A.T. Hopper Operational formulas connected with two generalizations of Hermite polynomials Duke Math. J. 29 1962 51-63
12. C. Jordan Calculus of Finite Differences 2nd ed. 1960 Chelsea Publishing Company New York
13. R. Koekoek, R.F. Swarrtow, The Askey-scheme of hypergeometric orthogonal polynomials and its q -analogue, Reports of the Faculty of Technical Mathematics and Informatics, No. 98-17. Delft University of Technology, Delft, 1998.
14. G. Markowsky Differential operators and the theory of binomial enumeration J. Math. Anal. Appl. 63 1978 145-155
15. P.I. Pastro Orthogonal polynomials and some q -beta integrals of Ramanujan J. Math. Anal. Appl. 112 1985 517-540
16. A. Ronveaux, Orthogonal polynomials: Connection and linearization coefficients, in: M. Alfaro, et al. (Eds.), Proceedings of the International Workshop on Orthogonal Polynomials in Mathematical Physics, 24-26 June 1996, Leganés, Madrid, Spain.
17. A. Ronveaux, S. Belmehdi, E. Godoy, A. Zarzo, Recurrence relation approach for connection coefficients. Application to classical discrete orthogonal polynomials, Proceedings of the International Workshop on Symmetries and Integrability of Difference Equations, CRM Proceedings and Lecture Notes Series, vol. 9, American Mathematical Society, Providence, RI, 1996, pp. 321-337.
18. G.C. Rota D. Kahaner A. Odlyzko On the foundations of combinatoric theory VIII Finite operator calculus J. Math. Anal. Appl. 42 1973 684-760
19. C. Runge Über eine besondere Art von Integralgleichungen Math. Ann. 75 1914 130-132
20. J. Sánchez-Ruiz J.S. Dehesa Some connection and linearization problems for polynomials in and beyond the Askey scheme J. Comput. Appl. Math. 133 2001 579-591
21. H.M. Srivastava H.L. Manocha A Treatise On Generating Functions 1984 Wiley New York, Chichester, Brisbane, Toronto
22. J.F. Steffensen The poweroid, an extension of the mathematical notion of power Acta Math. 73 1941 333-366
23. G. Szegö, Orthogonal Polynomials, 4th ed., American Mathematical Society Colloqium Publication, vol. 23, American Mathematical Society, New York, 1975.
24. F. Vogl On the uniform approximation of a class of analytic functions by Bruwier series J. Approx. Theory 107 2000 L281-L292
25. A. Zarzo I. Area E. Godoy A. Ronveaux Results on some inversion problems for classical continuous and discrete orthogonal polynomials J. Phys. A: Math. Gen. 30 1997 L35-L40