W.Y.C. Chen and Z.-G. Liu,
Parameter augmentation for basic hypergeometric series II,
J. Combin. Theory Ser. A 80(2) (1997) 175-195.

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, The generalized Hahn polynomials, TWMS J. Appl. Eng. Math. 5 (2015) 231-248.

3. M.A. Abdlhusein, The new application of the Cauchy operator, Journal of Zankoi Sulaimani, Part-A (2015) 193-204.

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

5. I. Ahmed, A study of Hermite polynomials and its generalizations, Master Thesis, Aligarh Muslim University, 2008.

6. S.A. Ali and A. Agnihotri, Certain basic hypergeometric series identities through q-exponential operator technique, International Bulletin of Mathematical Research 1 (2014) 49-53.

7. S.A. Ali and A. Agnihotri, Parameter augmentation for basic hypergeometric series by Cauchy operator, Palest. J. Math. 6 (2017) 159-164.

8. J. Cao, New proofs of generating functions for Rogers¨CSzegö polynomials, Appl. Math. Comput. 207 (2009) 486-492.

9. J. Cao, Bivariate generating functions for Rogers¨CSzegö polynomials, Appl. Math. Comput. 217 (2010) 2209-2216.

10. J. Cao, Notes on Carlitz's q-operators, Taiwanese J. Math. 14 (2010) 2229-2244.

11. J. Cao, Alternative proofs of generating functions for Hahn polynomials and some applications, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14 (2011) 571-590.

12. J. Cao, Moments for generating functions of Al-Salam-Carlitz polynomials, Abstr. Appl. Anal. (2012) Art. ID 548168, 18 pp.

13. J. Cao, A note on q-integrals and certain generating functions, Stud. Appl. Math. 131 (2013) 105-118.

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

15. J. Cao, A note on generalized q-difference equations for <q-beta and Andrews¨CAskey integral, J. Math. Anal. Appl. 412 (2014) 841-851.

16. J. Cao and Z.-H. Shen, On q-integral representations for q-Hahn and Askey-Wilson polynomials and certain generating functions, Appl. Math. E-Notes 17 (2017) 186-198.

17. J. Cao and X.-L. Zhao, Exponential operator decomposition for Carlitz type generating functions, Ars Combin. 116 (2014) 245-255.

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

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

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

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

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

23. T. Ernst, The history of q-calculus and a new method, Department of Mathematics, Uppsala University, 2000.

24. J.-P. Fang, q-Differential operator identities and applications, J. Math. Anal. Appl. 332 (2007) 1393-1407.

25. J.-P. Fang, Remarks on a generalized q-difference equation, J. Difference Equ. Appl. 21 (2015) 934-953.

26. J.-P. Fang, Generalizations of Milne's $\dpi{110}&space;U(n+1)$ q-Chu-Vandermonde summation, Czechoslovak Math. J. 66(141) (2016) 395-407.

27. V.J.W. Guo, Elementary proofs of some q-identities of Jackson and Andrews¨CJain, Discrete Math. 295 (2005) 63-74.

28. Z.Y. Jia, Two new q-exponential operator identities and their applications, J. Math. Anal. Appl. 419 (2014) 329-338.

29. Z.Y. Jia, A new extension of the nonterminating 6φ5 summation via q-difference equation, Taiwanese J. Math., to appear.

30. C. Krattenthaler and K.S. Rao, Automatic generation of hypergeometric identities by the beta integral method, J. Comput. Appl. Math. 160 (2003) 159-173.

31. A. Kumar, M.S. Khan and K.P. Yadav, Parameter augmentation for some basic hypergeometric series identities, J. Math. Comput. Sci. 2 (2012) 1532-1538.

32. N.N. Li and W. Tan, Two generalized q-exponential operators and their applications, Adv. Difference Equ. (2016) Paper No. 53, 14 pp.

33. Z.-G. Liu, Some operator identities and q-series transformation formulas, Discrete Math. 265 (2003) 119-139.

34. Z.-G. Liu, An identity of Andrews and the Askey-Wilson integral, Ramanujan J. 19 (2009) 115-119.

35. Z.-G. Liu, Two q-difference equations and q-operator identities, J. Difference Equ. Appl. 16 (2010) 1293-1307.

36. Z.-G. Liu, An extension of the non-terminating $\dpi{110}&space;_6\phi_5$ summation and the Askey¨CWilson polynomials, J. Difference Equ. Appl. 17 (2011) 1401-1411.

37. Z.-G. Liu, On the q-partial differential equations and q-series, In: The Legacy of Srinivasa Ramanujan, 213-250, Ramanujan Math. Soc. Lect. Notes Ser. 20, Ramanujan Math. Soc. Mysore, 2013.

38. Z.-G. Liu and J. Zeng, Two expansion formulas involving the Rogers¨CSzegö polynomials with applications, Int. J. Number Theory 11 (2015) 507-525.

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

40. Y.-P. Mu, Parameter augmentation and the q-Gosper algorithm, J. Symbolic Comput. 43 (2008) 874-882.

41. K.N. Murthy, A study of the theory of basic hypergeometric series and allied topics, Ph.D. Thesis, University of Mysore, 2013.

42. H.L. Saad and M.A. Abdlhusein, The q-exponential operator and generalized Rogers-Szegö polynomials, J. Adv. Math. 8 (2014) 1440-1455.

43. H.L. Saad and F.A. Reshem, The operator $\dpi{110}&space;G(a,b,D_q)$ for the polynomials $\dpi{110}&space;W_n(x,y,a,b;q)$, Journal of Advances in Mathematics 9 (2015) 2888-2904.

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

45. 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.

46. M.J. Wang, A generalization of the q-Pfaff-Saalsch¨¹tz formula, Contrib. Discret. Math. 3 (2008) 25-30.

47. M.J. Wang, Generalizations of Milne's $\dpi{110}&space;U(n+1)$ q-binomial theorems, Comput. Math. Appl. 58 (2009) 80-87.

48. M.J. Wang, q-integral representation of the Al-Salam-Carlitz polynomials, Appl. Math. Lett. 22 (2009) 943-945.

49. C.H. Zhang, Parameter augmentation for two formulas, Electron. J. Combin. 13 (2006) Note 19, 5 pp.

50. C.H. Zhang and Z.Z. Zhang, Extensions of two q-series identities, Adv. Stud. Contemp. Math. (Kyungshang) 13 (2006) 81-85.

51. Z.Z. Zhang, Some $\dpi{110}&space;_3\psi_3$ transformations formulas related to Bailey's $\dpi{110}&space;_2\psi_2$, Ars Combin. 78 (2006) 257-265.

52. Z.Z. Zhang, Operator identities and several $\dpi{110}&space;U(n+1)$ generalizations of the Kalnins¨CMiller transformations, J. Math. Anal. Appl. 324 (2006) 1152-1167.

53. Z.Z. Zhang and M.X. Liu, Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem, Discrete Math. 306 (2006) 1424-1437.

54. Z.Z. Zhang and J.S. Pang, Several q-series identities related to Jackson's, Ars Combin. 102 (2011) 139-145.

55. Z.Z. Zhang and J. Wang, Two operator identities and their applications to terminating basic hypergeometric series and q-integrals, J. Math. Anal. Appl. 312 (2005) 653-665.

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

57. Z.Z. Zhang and J.Z. Yang, Several q-series identities from the Euler expansions of $\dpi{110}&space;(a;q)_{\infty}$ and $\dpi{110}&space;{1}/{(a;q)_{\infty}}$, Arch. Math. (Brno) 45 (2009) 47-58.

58. Z.Z. Zhang and J.Z. Yang, On two identities of Fu and Lascoux, Adv. Stud. Contemp. Math. (Kyungshang) 18 (2009) 59-67.

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

60. J.-M. Zhu, The solutions of four q -functional equations, arXiv:1001.0299.

61. ·¿½£Æ½, q-Î¢·ÖËã×ÓºãµÈÊ½µÄÓ¦ÓÃ, »ª¶«Ê¦·¶´óÑ§Ñ§±¨ (×ÔÈ»¿ÆÑ§°æ) (2008) 20-24.

62. ÕÅÖ®Õý, Ñî¼ÌÕæ, Ë«²ÎÊýÓÐÏÞ q Ö¸ÊýËã×Ó¼°ÆäÓ¦ÓÃ, ÊýÑ§Ñ§±¨ 53 (2010) 1007-1018.