W.Y.C. Chen, A.M. Fu and B.Y. Zhang,
The homogeneous q-difference operator,
Adv. Appl. Math. 31 (2003) 659-668.

Cited by

  1. M.A. Abdlhusein, The Euler operator for basic hypergeometric series, Int. J. Adv. Appl. Math. Mech. 2 (2014) 42-52.

  2. M.A. Abdlhusein, Two operator representations for the trivariate q-polynomials and Hahn polynomials, Ramanujan J. 40 (2016) 491-509.

  3. S. Arjika, Certain generating functions for Cigler's polynomials, Montes Taurus J. Pure Appl. Math. 3(3) (2021) 284-296.

  4. S. Arjika and Z. Mouayn, Connection formulae for trivariate q-polynomials, arXiv:2205.00713.

  5. J. Cao, q-difference equations for generalized homogeneous q-operators and certain generating functions, J. Differ. Equ. Appl. 20 (2014) 837-851.

  6. J. Cao, Homogeneous q-difference equations and generating functions for q-hypergeometric polynomials, Ramanujan J. 40 (2016) 177-192.

  7. J. Cao, Homogeneous q-partial difference equations and some applications, Adv. in Appl. Math. 84 (2017) 47-72.

  8. V. Chandrasekar and K. Suresh, Theory and applications of generalized q-derivative operator, Int. J. Pure Appl. Math. 101 (2015) 963-973.

  9. S.H.L. Chen, W.Y.C. Chen, A.M. Fu and W.J.T. Zang, The algorithm Z and Ramanujan's summation, Ramanujan J. 25 (2011) 37-47.

  10. S.H.L. Chen and A.M. Fu, An 4n-point interpolation formula for certain polynomials, arXiv:1009.2594.

  11. V.Y.B. Chen and N.S.S. Gu, The Cauchy operator for basic hypergeometric series, Adv. in Appl. Math. 41 (2008) 177-196.

  12. W.Y.C. Chen and A.M. Fu, Cauchy augmentation for basic hypergeometric series, Bull. Lond. Math. Soc. 36 (2004) 169-175.

  13. W.Y.C. Chen, H.L. Saad and L.H. Sun, The bivariate Rogers–Szegö polynomials, J. Phys. A: Math. Theor. 40 (2007) 6071-6084.

  14. W.Y.C. Chen, H.L. Saad and L.H. Sun, An operator approach to the Al-Salam–Carlitz polynomials, J. Math. Phys. 51 (2010) 043502, 13 pp.

  15. D. Lu, q-difference equation and the Cauchy operator identities, J. Math. Anal. Appl. 359 (2009) 265-274.

  16. H.L. Saad, On the Cauchy polynomials, International Mathematical Forum 9 (2014) 1695-1706.

  17. H.L. Saad and A.A. Sukhi, The q-exponential operator, Appl. Math. Sci 7 (2005) 6369-6380.

  18. H.L. Saad and A.A. Sukhi, Another homogeneous q-difference operator, Appl. Math. Comput. 215 (2010) 4332-4339.

  19. H.M. Srivastava and M.A. Abdlhusein, New forms of the cauchy operator and some of their applications, Russ. J. Math. Phys. 23 (2016) 124-134.

  20. X.-F. Wang and J. Cao, q-difference equations for the generalized Cigler's polynomials, J. Difference Equ. Appl. 24 (2018) 479-502.

  21. G.B.A. Xavier, T.G. Gerly, and H. Nasira Begum, Finite series of polynomials and polynomial factorials arising from generalized q-difference operator, Far East Journal of Mathematical Sciences 94 (2014) 47-63.

  22. Z.Z. Zhang and T.Z. Wang, Operator identities involving the bivariate Rogers–Szegö polynomials and their applications to the multiple q-series identities, J. Math. Anal. Appl. 343 (2008) 884-903.

  23. Y. Zhou and Q.M. Luo, Some new generating functions for q-Hahn polynomials, J. Appl. Math. 2014 (2014) Art. ID 419365, 5 pp.

  24. 张之正, 杨继真, 双参数有限 q 指数算子及其应用, 数学学报 53 (2010) 1007-1018.