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THE q-DEFORMED GAMMA FUNCTION AND q-DEFORMED POLYGAMMA FUNCTION
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 Title & Authors
THE q-DEFORMED GAMMA FUNCTION AND q-DEFORMED POLYGAMMA FUNCTION
Chung, Won Sang; Kim, Taekyun; Mansour, Toufik;
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 Abstract
In this paper, we rederive the identity ${\Gamma}_q(x){\Gamma}_q(1-x)
 Keywords
q-gamma function;q-polygamma function;
 Language
English
 Cited by
1.
INEQUALITIES FOR THE (q, k)-DEFORMED GAMMA FUNCTION EMANATING FROM CERTAIN PROBLEMS OF TRAFFIC FLOW,;;

호남수학학술지, 2016. vol.38. 1, pp.9-15 crossref(new window)
1.
Inequalities for q-gamma function ratios, Analysis and Mathematical Physics, 2017, 1664-235X  crossref(new windwow)
 References
1.
M. Arik and D. Coon, Hilbert spaces of analytic functions and generalized coherent states, J. Mathematical Phys. 17 (1976), no. 4, 524-527. crossref(new window)

2.
R. Askey, The q-gamma and q-beta functions, Appl. Anal. 8 (1978), no. 2, 125-141. crossref(new window)

3.
N. M. Atakishiyev, A. Frank, and K. B. Wolf, A simple difference realization of the Heisenberg q-algebra, J. Math. Phys. 35 (1994), no. 7, 3253-3260. crossref(new window)

4.
R. W. Gosper, Experiments and Discoveries in q-Trigonometry, In Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, Proceedings of the Conference Held at the University of Florida, Gainesville, FL, 1999.

5.
F. H. Jackson, A generalization of the functions ${\Gamma}(n)\;and\;x^n$, Proc. Roy. Soc. London. 74 (1904), 64-72. crossref(new window)

6.
F. H. Jackson, The basic gamma function and the elliptic functions, Proc. Roy. Soc. London. A 76 (1905), 127-144. crossref(new window)

7.
T. Kim, q-Volkenborn integration, Russ. J. Math. Phys. 9 (2002), no. 3, 288-299.

8.
T. Kim and C. Adiga, On the q-analogue of gamma functions and related inequalities, J. Inequal. Pure Appl. Math. 6 (2005), no. 4, Article 118, 4 pp.

9.
A. Macfarlane, On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q, J. Phys. A 22 (1989), no. 21, 4581-4588. crossref(new window)

10.
M. Mansour, An asymptotic expansion of the q-gamma function ${\Gamma}_q(x)$, J. Nonlinear Math. Phys. 13 (2006), no. 4, 479-483. crossref(new window)

11.
T. Mansour and A. Shabani, Some inequalities for the q-digamma function, J. Inequal. Pure Appl. Math. 10 (2009), no. 1, Article 12, 8 pp.

12.
S.-H. Rim and T. Kim, A note on the q-analogue of p-adic log-gamma function, Adv. Stud. Contemp. Math. 18 (2009), no. 2, 245-248.

13.
A. Salem, An infinite class of completely monotonic functions involving the q-gamma function, J. Math. Anal. Appl. 406 (2013), no. 2, 392-399. crossref(new window)

14.
A. Salem, A completely monotonic function involving q-gamma and q-digamma functions, J. Approx. Theory 164 (2012), no. 7, 971-980. crossref(new window)

15.
W. T. Sulaiman, Some inequalities for the q-digamma functions, J. Concr. Appl. Math. 10 (2012), no. 3-4, 301-308.

16.
N. J. Sloane, The On-Line Encyclopedia of Integer Sequences, http://oeis.org, 2010.

17.
J. Thomae, Beitrage zur Theorie der durch die Heinesche Reihe, J. Reine Angew. Math. 70 (1869), 258-281.