SOME APPLICATIONS OF q-DIFFERENTIAL OPERATOR

Title & Authors
SOME APPLICATIONS OF q-DIFFERENTIAL OPERATOR
Fang, Jian-Ping;

Abstract
In this paper, we use q-differential operator to recover the finite Heine $\small{_2\Phi_1}$ transformations given in [3]. Applying that, we also obtain some terminating q-series transformation formulas.
Keywords
q-series;q-differential operator;Rogers-Ramanujan type identity;
Language
English
Cited by
1.
Q-FRACTIONAL INTEGRALS AND SPECIAL FUNCTIONS,;

Advanced Studies in Contemporary Mathematics, 2014. vol.24. 1, pp.87-95
2.
ON SOME PROPERTIES OF THE GENERALIZED Q-MITTAG-LEFFLER FUNCTION,;

Advanced Studies in Contemporary Mathematics, 2015. vol.25. 1, pp.65-73
1.
Remarks on a generalizedq-difference equation, Journal of Difference Equations and Applications, 2015, 21, 10, 934
2.
Two generalized q-exponential operators and their applications, Advances in Difference Equations, 2016, 2016, 1
3.
Caputo type fractional difference operator and its application on discrete time scales, Advances in Difference Equations, 2015, 2015, 1
4.
Applications of a generalized q-difference equation, Advances in Difference Equations, 2014, 2014, 1, 267
5.
A note on generalized q-difference equations for q-beta and Andrews–Askey integral, Journal of Mathematical Analysis and Applications, 2014, 412, 2, 841
6.
q-Difference equation and q-polynomials, Applied Mathematics and Computation, 2014, 248, 550
7.
Generalizations of Milne’s U(n + 1) q-Chu-Vandermonde summation, Czechoslovak Mathematical Journal, 2016, 66, 2, 395
References
1.
G. E. Andrews, Enumerative proofs of certain q-identities, Glasgow Math. J. 8 (1967), 33-40.

2.
G. E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and its Applications, Vol. 2. Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976.

3.
G. E. Andrews, The finite Heine transformation, Preprint.

4.
G. E. Andrews and B. C. Berndt, Ramanujan's Lost Notebook, Part I, Springer, 2005.

5.
G. E. Andrews and S. O. Warnaar, The product of partial theta functions, Adv. in Appl. Math. 39 (2007), no. 1, 116–120.

6.
J.-P. Fang, A q-differential operator identity and its applications, J. East China Norm. Univ. Natur. Sci. Ed. 2008 (2008), no. 1, 20–24.

7.
J.-P. Fang, Extensions of q-Chu-Vandermonde's identity, J. Math. Anal. Appl. 339 (2008), no. 2, 845–852.

8.
G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.

9.
V. K. Jain, Some transformations of basic hypergeometric series and their applications, Proc. Amer. Math. Soc. 78 (1980), no. 3, 375–384.

10.
Z.-G. Liu, An expansion formula for q-series and applications, Ramanujan J. 6 (2002), no. 4, 429–447.

11.
Z.-G. Liu, Some operator identities and q-series transformation formulas, Discrete Math. 265 (2003), no. 1-3, 119–139.

12.
L. J. Rogers, On the expansion of some infinte products, Proc. London Math. Soc. 24 (1893), 337–352.

13.
A. V. Sills, Finite Rogers-Ramanujan type identities, Electron. J. Combin. 10 (2003), Research Paper 13, 122 pp.

14.
L. J. Slater, Further identies of the Rogers-Ramanujan type, Proc. London Math. Soc. (2) 54 (1952), 147–167.

15.
S. O.Warnaar, Partial theta functions. I. Beyond the lost notebook, Proc. London Math. Soc. (3) 87 (2003), no. 2, 363–395.