Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials

Journal of Physics A: Mathematical and General

Volumn 37, Issue 33, 2004, Pages 8045-8063

  Doha, E H ^a   Ahmed, H M ^b  

^a CAIRO UNIVERSITY   (Egypt)

^b Faculty of Industrial Education   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4344713401     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/33/006     Document Type: Article

References (58)

1. Abramowitz M and Stegun I A (ed) 1970 Handbook of Mathematical Functions (Appl. Maths Series vol 55) (New York: National Bureau of Standards)
2. Agarwal R P 1954 On Bessel polynomials Can. J. Math. 6 410-5
3. 2s J. Phys. A: Math. Gen. 29 7165-75
4. Al-Salam W 1957 The Bessel polynomials Duke Math. J. 24 529-45
5. Àlvarez-Nodarse, Yàñez R J and Dehesa J S 1998 Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials J. Comput. Appl. Math. 89 171-97
6. Andrews G E, Askey R and Roy R 1999 Special Functions (Cambridge: Cambridge University Press)
7. Area I, Godoy E, Ronveaux A and Zarzo A 1998 Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: discrete case J. Comput. Appl. Math. 89 309-25
8. Askey R and Gasper G 1971 Jacobi polynomials expansions of Jacobi polynomials with non-negative coefficients Proc. Camb. Phil. Soc. 70 243-55
9. Ben-Yu G 1998 Spectral Methods and Their Applications (London: World Scientific)
10. Cannon B 1937 On the convergence of series of polynomials Proc. London Math. Soc. 43 348-64
11. Canuto C, Hussaini M Y, Quarteroni A and Zang T A 1988 Spectral Methods in Fluid Dynamics (Berlin: Springer)
12. Carlitz L 1957 On the Bessel polynomials Duke Math. J. 24 151-62
13. Chihara T S 1978 An Introduction to Orthogonal Polynomials (New York: Gordon and Breach)
14. Coutsias E A, Hagstorm T and Torres D 1996 An efficient spectral methods for ordinary differential equations with rational function coefficients Math. Comput. 65 611-35
15. Doha E H 1990 An accurate solution of parabolic equations by expansion in ultraspherical polynomials J. Comput. Math. Appl. 19 75-88
16. Doha E H 1991 The coefficients of differentiated expansions and derivatives of ultraspherical polynomials J. Comput. Math. Appl. 21 115-22
17. Doha E H 1994 The first and second kinds Chebyshev coefficients of the moments of the general-order derivative of an infinitely differentiable function Int. J. Comput. Math. 51 21-35
18. Doha E H 1998 The ultraspherical coefficients of the moments of a general-order derivative of an infinitely differentiable function J. Comput. Appl. Math. 89 53-72
19. Doha E H 2000 The coefficients of differentiated expansions of double and triple ultraspherical polynomials Ann. Univ. Sci. Budapest, Sect. Comput. 19 57-73
20. Doha E H 2002a On the coefficients of differentiated expansions and derivatives of Jacobi polynomials J. Phys. A: Math. Gen. 35 3467-78
21. Doha E H 2002b On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations J. Comput. Appl. Math. 139 275-98
22. Doha E H 2003a Explicit formulae for the coefficients of integrated expansions for Jacobi polynomials and their integrals Integral Transforms Spec. Funct. 14 69-86
23. Doha E H 2003b On the connection coefficients and recurrence relations arising from expansions in series of Laguerre polynomials J. Phys. A: Math. Gen. 36 5449-62
24. Doha E H 2004a On the connection coefficients and recurrence relations arising from expansions in series of Hermite polynomials Integral Transforms Spec. Funct. 15 13-29
25. Doha E H 2004b On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials J. Phys. A: Math. Gen. 37 657-75
26. Doha E H and Abd-Elhameed W M 2002 Efficient spectral Galerkin-algorithms for direct solution of second-order equations using ultraspherical polynomials SIAM J. Sci. Comput. 24 548-71
27. Doha E H and Al-Kholi F M R 2001 An efficient double Legendre spectral method for parabolic and elliptic partial differential equations Int. J. Comput. Math. 78 413-32
28. Doha E H and El-Soubhy S I 1995 On the Legendre coefficients of the moments of general-order derivative of an infinitely differentiable function Int. J. Comput. Math. 56 107-22
29. Doha E H and Helal M A 1997 An accurate double Chebyshev spectral approximation for parabolic partial differential equations J. Egypt. Math. Soc. 5 83-101
30. Evans W D, Everitt W N, Kwon K H and Littlejohn L L 1993 Real orthogonalizing weights for Bessel polynomials J. Comput. Appl. Math. 49 51-7
31. Gasper G 1974 Project formulas for orthogonal polynomials of a discrete variable J. Math. Anal. Appl. 45 176-98
32. Godoy E, Ronveaux A, Zarzo A and Area I 1997 Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: continuous case J. Comput. Appl. Math. 84 257-75
33. Grosswald E 1978 Bessel polynomials Lecture Notes Math. 698 1-182
34. Haidvogel D B and Zang T 1979 The accurate solution of Poisson's equation by Chebyshev polynomials J. Comput. Phys. 30 167-80
35. Han S S and Kwon K H 1991 Spectral analysis of Bessel polynomials in Krein space Quaest. Math. 14 327-35
36. Helal M A 2001 A Chebyshev spectral method for solving Korteweg-de Vries equation with hydrodynamical application Chaos Solitons Fractals 12 943-50
37. Karageorghis A 1988a A note on the Chebyshev coefficients of the general-order derivative of an infinitely differentiable function J. Comput. Appl. Math. 21 129-32
38. Karageorghis A 1988b A note on the Chebyshev coefficients of the moments of the general-order derivative of an infinitely differentiable function J. Comput. Appl. Math. 21 383-6
39. Karageorghis A and Phillips T N 1989 On the coefficients of differentiated expansions of ultraspherical polynomials ICASE Report no 89-65 NASA Langley Research Center, Hampton, VA
40. Karageorghis A and Phillips T N 1992 Appl. Numer. Math. 9 133-41
41. Koepf W and Schmersau D 1998 Representations of orthogonal polynomials J. Comput. Appl. Math. 90 57-94
42. Krall H L and Frink O 1949 A new class of orthogonal polynomials: the Bessel polynomials Trans. Am. Math. Soc. 65 100-5
43. Lewanowicz S 2002 Recurrences of coefficients of series expansions with respect to classical orthogonal polynomials Appl. Math. 29 97-116
44. Lewanowicz S, Godoy E, Area I, Ronveaux A and Zarzo A 2000 Recurrence relations for coefficients of Fourier series expansions with respect to q-classical orthogonal polynomials Numer. Algorithms 23 31-50
45. Lewanowicz S and Woźny P 2001 Algorithms for construction of recurrence relations for the coefficients of expansions in series of classical orthogonal polynomials Preprint Institute of Computer Science University of Wroclaw online at http://www.ii.uni.wroc.pl/sle/publ.html
46. Luke Y L 1969 The Special Functions and Their Approximations vols 1 and 2 (New York: Academic)
47. Nassif M 1954 Note on the Bessel polynomials Trans. Am. Math. Soc. 77 408-12
48. Phillips T N 1988 On the Legendre coefficients of a general-order derivative of an infinitely differentiable function IMA. J. Numer. Anal. 8 455-9
49. Rainville E D 1960 Special Functions (New York: Macmillan)
50. Ronveaux A, Belmehdi S, Godoy E and Zarzo A 1996 Recurrence relation approach for connection coefficients. Applications to classical discrete orthogonal polynomials CRM Proc. and Lecture notes vol 9 (Centre de Researches Mathématiques) pp 319-35
51. Ronveaux A, Zarzo A and Godoy E 1995 Recurrence relations for connection coefficients between two families of orthogonal polynomials J. Comput. Appl. Math. 62 67-73
52. Sánchez-Ruiz J and Dehesa J S 1998 Expansions in series of orthogonal polynomials J. Comput. Appl. Math. 89 155-70
53. Siyyam H I and Syam M I 1997 An accurate solution of Poisson equation by the Chebyshev-Tau methods J. Comput. Appl. Math. 85 1-10
54. Szegö G 1985 Orthogonal Polynomials (American Mathematical Society Colloquium Publications vol 23) (Providence, RI: American Mathematical Society)
55. Voigt R G, Gottlieb D and Hussaini M Y 1984 Spectral Methods for Partial Differential Equations (Philadelphia, PA: SIAM)
56. Whittaker J M 1949 Sur les séries de base de polynomes quelconques (Paris: Gauthier-Villars)
57. Wolfram Research Inc. 1999 Mathematica Version 4.0 (Wolfram Research Champaign)
58. Zarzo A, Area I, Godoy E and Ronveaux A 1997 Results for some inversion problems for classical continuous and discrete orthogonal polynomials J. Phys. A: Math. Gen. 30 35-40