JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON p, q-DIFFERENCE OPERATOR
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON p, q-DIFFERENCE OPERATOR
Corcino, Roberto B.; Montero, Charles B.;
  PDF(new window)
 Abstract
In this paper, we define a , -difference operator and obtain an explicit formula which is used to express the , -analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the , -difference operator. Explicit formulas for the non-central -Stirling numbers of the second kind and non-central -Lah numbers are derived using the new -analogue of Newton`s interpolation formula. Moreover, a , -analogue of Newton`s interpolation formula is established.
 Keywords
, -difference operator;-Stirling numbers;-Lah numbers;Newton`s interpolation formula;exponential generating function;
 Language
English
 Cited by
 References
1.
L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948), 987-1000. crossref(new window)

2.
K. Conrad, A q-analogue of Mahler expansions I, Adv. Math. 153 (2000), no. 2, 185- 230. crossref(new window)

3.
R. B. Corcino, On p, q-binomial coefficients, Integers 8 (2008), A29, 16 pp.

4.
R. B. Corcino, L. C. Hsu, and E. L. Tan, A q-analogue of generalized Stirling numbers, Fibonacci Quart. 44 (2006), no. 2, 154-165.

5.
R. B. Corcino and C. Montero, A p, q-analogue of the generalized Stirling numbers, JP J. Algebra Number Theory Appl. 15 (2009), no. 2, 137-155.

6.
A. De Medicis and P. Leroux, Generalized Stirling numbers, convolution formulae and p, q-analogues, Canad. J. Math. 47 (1995), no. 3, 474-499. crossref(new window)

7.
L. C. Hsu and P. J.-S. Shiue, A unified approach to generalized Stirling numbers, Adv. in Appl. Math. 20 (1998), no. 3, 366-384. crossref(new window)

8.
M. S. Kim and J. W. Son, A note on q-difference operators, Commun. Korean Math. Soc. 17 (2002), no. 3, 423-430. crossref(new window)

9.
P. Leroux, Reduced matrices and q-log-concavity properties of q-Stirling numbers, J. Combin. Theory Ser. A 54 (1990), no. 1, 64-84. crossref(new window)

10.
D. S. Moak, The q-analogue of the Lagurre polynomials, J. Math. Anal. Appl. 81 (1981), no. 1, 20-47. crossref(new window)

11.
J. B. Remmel and M. L. Wachs, Rook theory, generalized Stirling numbers and (p, q)- analogues, Electron. J. Combin. 11 (2004), no. 1, Research Paper 84, 48 pp.

12.
S.-Z. Song, G.-S. Cheon, Y.-B. Jun, and L. B. Beasley, A q-analogue of the generalized factorial numbers, J. Korean Math. Soc. 47 (2010), no. 3, 645-657.

13.
M. Wachs and D. White, p, q-Stirling numbers and set partition statistics, J. Combin. Theory Ser. A 56 (1991), no. 1, 27-46. crossref(new window)