q-Taylor and interpolation series for Jackson q-difference operators

Journal of Mathematical Analysis and Applications

Volumn 344, Issue 1, 2008, Pages 472-483

  Annaby, M H ^a   Mansour, Z S ^a  

^a CAIRO UNIVERSITY   (Egypt)

Author keywords

Jackson q difference operator; q Taylor series

Indexed keywords

EID: 42649085010     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.02.033     Document Type: Article

References (19)

1. M.H. Abu-Risha, M.H. Annaby, M.E.H. Ismail, Z.S. Mansour, Existence and uniqueness theorems of q-difference equations, submitted for publication
2. Al-Salam W.A. q-analogue of the Cauchy formula. Proc. Amer. Math. Soc. 17 (1966) 616-621
3. Al-Salam W.A., and Verma A. A fractional Leibniz q-formula. Pacific J. Math. 60 (1975) 1-9
4. Bezivin J.P. Sur les équations fonctionelles p-adiques aux q-différences. Collect. Math. 43 2 (1992) 125-140
5. Bouzeffour F. Interpolation of entire functions, product formula for basic sine function. J. Nonlinear Math. Phys. 13 2 (2006) 293-301
6. Gasper G., and Rahman M. Basic Hypergeometric Series (2004), Cambridge University Press, Cambridge
7. Hahn W. Über die höheren Heineschen Reihen und eine einheitliche Theorie der sogenannten speziellen Funktionen. Math. Nachr. 3 (1950) 257-294
8. Hayman W.K. On the zeros of q-Bessel function. Contemp. Math. vol. 382 (2005) 205-216
9. Ismail M.E.H. The Askey-Wilson operator and summation theorems. Contemp. Math. vol. 190 (1995) 171-178
10. Ismail M.E.H., and Stanton D. Applications of q-Taylor theorems. J. Comput. Appl. Math. 153 (2003) 259-272
11. Ismail M.E.H., and Stanton D. q-Taylor theorems, polynomial expansions, and interpolation of entire functions. J. Approx. Theory 123 (2003) 125-146
12. n. Proc. Roy. Soc. London 74 (1904) 64-72
13. Jackson F.H. On q-functions and a certain difference operator. Trans. Roy. Soc. Edinburgh 46 (1908) 64-72
14. Jackson F.H. q-form of Taylor's theorem. Messenger Math. 39 (1909) 62-64
15. Jackson F.H. On q-definite integrals. Q. J. Pure Appl. Math. 41 (1910) 193-203
16. López B., Marco J.M., and Parcet J. Taylor series for the Askey-Wilson operator and classical summation formulas. Proc. Amer. Math. Soc. 134 8 (2006) 2259-2270
17. Marco J.M., and Parcet J. A new approach to the theory of classical hypergeometric polynomials. Trans. Amer. Math. Soc. 358 1 (2006) 183-214
18. Ramis J.P. About the growth of entire functions solutions of linear algebraic q-difference equations. Ann. Fac. Sci. Toulouse Math. 1 6 (1992) 53-94
19. Welter M. Interpolation of entire functions on regular sparse sets and q-Taylor series. J. Theor. Nombres Bordeaux 17 (2005) 397-404