Applications of q-Taylor theorems

Journal of Computational and Applied Mathematics

Volumn 153, Issue 1-2, 2003, Pages 259-272

  Ismail, Mourad E H ^a   Stanton, Dennis ^b  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Askey Wilson operators; Connection relations; Polynomial bases; q exponential function; Summation theorems

Indexed keywords

LINEARIZATION; MATHEMATICAL TRANSFORMATIONS; POLYNOMIALS;

TAYLOR SERIES;

THEOREM PROVING;

MATHEMATICAL ANALYSIS;

EID: 0037381925     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(02)00644-1     Document Type: Article

References (14)

1. G.E. Andrews, R.A. Askey, R. Roy, Special Functions, Cambridge University Press, Cambridge, 1999.
2. R.A. Askey, M.E.H. Ismail, A generalization of ultraspherical polynomials, in: P. Erdö (Ed.), Studies in Pure Mathematics, Birkhauser, Basel, 1983, pp. 55-78.
3. R.A. Askey, J.A. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 319 (1985) 1-55.
4. G. Gasper, M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.
5. M.E.H. Ismail, The Askey-Wilson operator and summation theorems, in: M. Ismail, M.Z. Nashed, A. Zayed, A. Ghaleb (Eds.), Mathematical Analysis, Wavelets, and Signal Processing, Contemporary Mathematics, Vol. 190, American Mathematical Society, Providence, RI, 1995, pp. 171-178.
6. M.E.H. Ismail, D. Stanton, Addition theorems for the q-exponential function, in: M.E.H. Ismail, D. Stanton (Eds.), q-Series from a Contemporary Perspective, Contemporary Mathematics, Vol. 254, American Mathematical Society, Providence, RI, 2000, pp. 235-245.
7. M.E.H. Ismail, D. Stanton, q-integral and moment representations for q-orthogonal polynomials, Canad. J. Math. 54 (2002) 709-735.
8. M.E.H. Ismail, D. Stanton, q-Taylor theorems, polynomial expansions, and interpolation of entire functions, preprint.
9. M.E.H. Ismail, R. Zhang, Diagonalization of certain integral operators, Adv. in Math. 109 (1994) 1-33.
10. S.C. Jing, H.Y. Fan, q-Taylor's formula with its q-remainder, Comm. Theoret. Phys. 23 (1995) 117-120.
11. M. Rahman, The linearization of the product of continuous q-Jacobi polynomials, Canad. J. Math. 33 (1981) 255-284.
12. Z. Sui, G. Yu, Z. Yu, q,s-Taylor's formula with q,s remainder, Comm. Theoret. Phys. 30 (1998) 133-136.
13. S.K. Suslov, Addition theorems for some q-exponential and trigonometric functions, Methods Appl. Anal. 4 (1997) 11-32.
14. S.K. Suslov, Some expansions in basic Fourier series and related topics, J. Approx. Theory 115 (2002) 289-353.