Asymptotic approximations in quantum calculus

Journal of Nonlinear Mathematical Physics

Volumn 12, Issue 4, 2005, Pages 586-606

  Fitouhi, Ahmed ^a   Brahim, Kamel ^b   Bettaibi, Néji ^c  

^a FACULTÉ DES SCIENCES DE TUNIS   (Tunisia)

^b Institut Preparatoire Aux Etudes d'Ingenieurs de Tunis   (Tunisia)

^c Institut Preparatoire aux Etudes d'Ingenieurs de Nabeul   (Tunisia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 30444461502     PISSN: 14029251     EISSN: 14029251     Source Type: Journal    
DOI: 10.2991/jnmp.2005.12.4.11     Document Type: Article

References (17)

1. De Sole A and Kac V G, On integral representations of q-gamma and q-beta functions, preprint arXiv:math.QA/0302032.
2. Ernst T, A new notation for q-calculus and a new q-Taylor formula, U. U. D. M. Report 1999:25, ISSN 1101-3591, Uppsala University, 1999.
3. Ernst T, The history of q-Calculus and a New Method, U. U. D. M. Report 2000:16, ISSN 1101-3591 Uppsala University, 2000.
4. Ernst T, A method for q-Calculus, J. Nonlinear Math. Phys. 10 (2003), 487-525.
5. Fitouhi A, Bettaibi N and Brahim K, The Mellin transform in Quantum Calculus, to appear in Constructive Approximation.
6. Fitouhi A and Bouzeffour F, q-cosine Fourier transform and q-heat equation, to appear in Ramanujan Journal.
7. α Bessel function, J. Approx. Theory 115 (2002), 144-166.
8. Gasper G and Rahmen M, Basic hypergeometric series, Encyclopedia of Mathematics and its application 35, Cambridge University Press, Cambridge, 1990.
9. v+ax(x), and associated orthogonal polynomials, J. Math. Anal. Appl. 86 (1982), 1-19.
10. Jackson F H, On a q-definite integrals, Q. J. Pure Appl. Math. 41 (1910), 193-203.
11. Kac V G and Cheung P, Quantum Calculus, Springer-Verlag, New York, 2002.
12. Koornwinder T H, q-Special Functions, a Tutorial, in Deformation theory and quantum groups with applications to mathematical physics, Contemp. Math. 134, Editors: Gerstenhaber M and Stasheff J, American Mathematical Society, Providence, 1992, 141-142.
13. Koornwinder T H, Special Functions and q-Commuting Variables, in Special Functions, q-Series and related Topics, Fields Inst. Commun. 14, Editors: Ismail M E H, Masson D R and Rahman M, American Mathematical Society, Providence, 1997, 131-166; arXiv:q-alg/9608008.
14. Koornwinder T H and Swarttouw R F, On q-analogues of the Fourier and Hankel transforms, Trans. Amer. Math. Soc. 333 (1992), 445-461.
15. Moak D S, The q-analogue of Stirlings formula, Rocky Mt. J. Math. 14 (1984), 403-413.
16. Olde Daalhuis A B, Asymptotic expansions for q-Gamma, q-exponentials, and q-Bessel functions, J. Math. Anal. Appl. 186 (1994), 896-913.
17. Wong R, Asymptotic approximations of integrals (Computer Science and Scientific Computing), Academic Press, New York, 1989.