DOI QR코드

DOI QR Code

특수함수의 q-유사에 관한 소고

손진우

  • Published : 2005.10.01

Abstract

본 논문에서는 양정수n의 q-유사를 이용한 q-이항정리, q-차례곱, q-차분 연산자, q-적분에 관한 최근의 기본개념을 정리하고, 이를 적용하여 q-베타함수와 q-감마함수의 새로운 q-유사에 대한 특징을 간략하게 논한다.

Keywords

q-유사;q-차분 연산자;q-베타함수;q-감마함수

References

  1. M. Aigner, Combinatorial Theory, Springer-Verlag, New York, 1979
  2. G. E. Andrews, R. Askey, and R. Roy, Special; Functions Cambridge, England, Cambridge University Press, 1999
  3. L. Carlitz, q-Bernouili numbers and polynomials, Duke Math. J. 15 (1948), 987-1000 https://doi.org/10.1215/S0012-7094-48-01588-9
  4. L. Carlitz, Multiplication formulas for products of Bernoulli and Euler polynomials, Pacific J. Math. 9 (1959), 661-666 https://doi.org/10.2140/pjm.1959.9.661
  5. A. Cauchy, Oeuvres, Ser. I, Vol. 8, Gauthier-Villars, Paris, 1893
  6. K. Conrad, A q-unaloque of Mahler expansions I, Adv. Math. 153 (2000), 185-230 https://doi.org/10.1006/aima.1999.1890
  7. K. Dilcher, On Generalized Gamma functions related to the Laurent coefficients of the Riemann zeta function, Aequationes Math. 48 (1994), 55-85 https://doi.org/10.1007/BF01837979
  8. H. Exton, q-Hypergeometric Functions and Applications, New York, Halstead Press, 1983
  9. R. Fray, Congruence properties of ordinary and q-binomial coefficients, Duke Math. J. 34 (1967), 467-480 https://doi.org/10.1215/S0012-7094-67-03452-7
  10. G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge Univ. Press, Cambridge, Uk, 1990
  11. L. Hellstrom and S. D. Silvestrov, Commuting Elements in q-Deformed Heisenberg Algebras, World Scientific Publishing co.pte.Ltd 2000
  12. M. E. H. Ismail, D. R. Masson, and M. Rahman, Special Functions, q-Series and Related Topics, Amer. Math. Soc. 1997
  13. F. H. Jackson, On q-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh 46 (1908), 253-281
  14. C. Jordan, Calculus of finite differences, Third Edition, Introduction by Harry C. Carver, Chelsea Publishing Co., New York, 1965
  15. N. Koblitz, q-Extension o] the p-adic gamma junction, Trans. Amer. Math. Soc. 260 (1980),449-457 https://doi.org/10.2307/1998014
  16. R. Koekoek and R. F. Swarttouw, The Askey-Scheme of Hypergeometric Orthogonal Polynomials and its q-Analogue, Delft, Netherlands: Technische Universiteit Delft, Faculty of Technical Mathematics and Informatics Report 98-17, p.7, 1998
  17. W. Koepf, Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, p.26, 1998
  18. C. Lee, Introduction to Combinatorics, Kyowoo Publishing Company, Seoul Korea, 2000
  19. N. Ja. Vilenkin and A. U. Klimyk, Representation of Lie Groups and Special Functions. Vol.III. Kluwer Academic Publishers. Netherlands. 1991
  20. V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov p-Adic Analysis and Mathematical Physics, Series on Soviet & East European Mathematics, Vol. I, World Scientific, Singapore, 1994
  21. M.-S. Kim and J.-W. Son, A note on q-difference operators, Commun. Korean Math. Soc. 17 (2002), 423-430 https://doi.org/10.4134/CKMS.2002.17.3.423
  22. A. N. Kirillov, Dilogarithm identities, Progress Theor. Phys. Supplement, 118 (1995), 61-142 https://doi.org/10.1143/PTPS.118.61