본문 바로가기
KERD
논문KCI 등재

THE q-DEFORMED GAMMA FUNCTION AND q-DEFORMED POLYGAMMA FUNCTION

0

조회

0

다운로드

1

인용

0

참고문헌

키워드

주제분류수학

초록

In this paper, we rederive the identity Γ(x)Γq(1 − x) = q sinq(qx) . Then, we give q-analogue of Gauss’ multiplication formula and study representation of q-oscillator algebra in terms of the q-factorial polynomials.

Abstract

In this paper, we rederive the identity Γ(x)Γq(1 − x) = q sinq(qx) . Then, we give q-analogue of Gauss’ multiplication formula and study representation of q-oscillator algebra in terms of the q-factorial polynomials.

참고문헌 (17)

  1. M. Arik, "Hilbert spaces of analytic functions and generalized coherent states", J. Mathematical Phys, 17(4), pp.524~527 (1976)
  2. R. Askey, "The q-gamma and q-beta functions", Appl. Anal, 8(2), pp.125~141 (1978)
  3. N. M. Atakishiyev, "A simple difference realization of the Heisenberg q-algebra", J. Math. Phys, 35(7), pp.3253~3260 (1994)
  4. R. W. Gosper, "Experiments and Discoveries in q-Trigonometry, In Symbolic Compu-tation, Number Theory, Special Functions, Physics and Combinatorics", Proceedings of the Conference Held at the University of Florida (1999)
  5. F. H. Jackson, "A generalization of the functions (n) and xn, Proc", Roy. Soc. London, 74, pp.64~72 (1904)
  6. F. H. Jackson, "The basic gamma function and the elliptic functions", Proc. Roy. Soc. London. A, 76, pp.127~144 (1905)
  7. T. Kim, "q-Volkenborn integration", Russ. J. Math. Phys, 9(3), pp.288~299 (2002)
  8. T. Kim, "On the q-analogue of gamma functions and related inequalities", J. Inequal. Pure Appl. Math, 6(4), pp.4~ (2005)
  9. A. Macfarlane, "On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q", J. Phys. A, 22(21), pp.4581~4588 (1989)
  10. M. Mansour, "An asymptotic expansion of the q-gamma function q(x)", J. Nonlinear Math. Phys, 13(4), pp.479~483 (2006)
  11. T. Mansour, "Some inequalities for the q-digamma function", J. Inequal. Pure Appl. Math, 10(1), pp.8~ (2009)
  12. 임석훈, "A note on the q-analogue of p-adic log-gamma function", Advanced Studies in Contemporary Mathematics, 18(2), pp.245~248 (2009), 장전수학회
  13. A. Salem, "An infinite class of completely monotonic functions involving the q-gamma function", J. Math. Anal. Appl, 406(2), pp.392~399 (2013)
  14. A. Salem, "A completely monotonic function involving q-gamma and q-digamma functions", J. Approx. Theory, 164(7), pp.971~980 (2012)
  15. W. T. Sulaiman, "Some inequalities for the q-digamma functions", J. Concr. Appl. Math, 10(3-4), pp.301~308 (2012)
  16. "The On-Line Encyclopedia of Integer Sequences"[URL]
  17. J. Thomae, "Beitrage zur Theorie der durch die Heinesche Reihe", J. Reine Angew. Math, 70, pp.258~281 (1869)

관련 논문AI추천

이 간행물의 다른 논문 (30건)