References

APPLICATIONS OF Q-DIFFERENTIAL OPERATOR


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[2] J. P. Fang, Extensions of q-Chu-Vandermonde’s identity, J. Math. Anal. Appl. 339(2) (2007), 845-852.

[3] J. P. Fang, q-Differential operator identities and applications, J. Math. Anal. Appl. 332(2) (2007), 1393-1407.

[4] N. J. Fine, Basic Hypergeometric Series and Applications, Mathematical Surveys, 27, Amer. Math. Soc. Providence, RI (1998).

[5] G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, Ma (1990).

[6] E. G. Kalnins and Jr. W. Miller, q-series and orthogonal polynomials associated with Barnes’ first lemma, SIAM J. Math. Anal. 19 (1998), 1216-1231.

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

[8] Z. G. Liu, An expansion formula for q-series and applications, The Ramanujan J. 6 (2002), 429-447.

[9] Z. G. Liu, A new proof of the Nassrallah-Rahman integral, Acta Math. Sinica 41 (1998), 405-410 (in Chinese).

[10] Z. G. Liu, An Identity For q-differential operators and it’s application, J. Systems Sci. Math. Sci. 18 (1998), 321-327 (in Chinese).

[11] M. Rahman and S. K. Suslov, Barnes and Ramanujan-type integrals on the q-linear lattice, SIAM J. Math. Anal. 25 (1994), 1002-1022.

[12] S. Roman, More on the umbral calculus, with emphasis on the q-umbral calculus, J. Math. Anal. Appl. 107 (1985), 222-254.

[13] S. Roman, The theory of the umbral calculus I, J. Math. Anal. Appl. 87 (1982), 58-115.

[14] G. N. Watson, The continuations of functions defined by generalized hypergeometric series, Trans. Camb. Phil. Soc. 21 (1910), 281-299.