Parameter Augmentation for Basic Hypergeometric Series, II

Journal of Combinatorial Theory. Series A

Volumn 80, Issue 2, 1997, Pages 175-195

  Chen, William Y C ^a,b   Liu, Zhi Guo ^c  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b NANKAI UNIVERSITY   (China)

^c Xinxiang Education College   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038877325     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcta.1997.2801     Document Type: Article

References (35)

1. Andrews G. E. q. Duke Math. J. 33:1966;575-581.
2. Andrews G. E. On the foundation of combinatorial theory V, Eulerian differential operators. Stud. Appl. Math. 50:1971;345-375.
3. Andrews G. E. Applications of basic hypergeometric functions. SIAM Rev. 16:1974;441-484.
4. Andrews G. E. The Theory of Partitions. Encylopedia of Mathematics and Its Applications. 1976;Addison-Wesley, Reading.
5. Andrews G. E. q. CBMS Regional Conference Lecture Series. 66:1986;Amer. Math. Soc, Providences.
6. Andrews G. E., Askey R. Anotherq. Proc. Amer. Math. Soc. 81:1981;97-100.
7. Askey R. An elementary evalution of a beta type integral. Indian J. Pure. Appl. Math. 14:1983;892-895.
8. Askey R., Ismail M. E. H. A generalization of ultraspherical polynomials. Erdös P. Studies in Pure Mathematics. 1983;55-78 Birkhäuser, Boston.
9. Askey R., Wilson J. Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Memoirs. Amer. Math. Soc. 54:1985.
10. Atakishiyev N. M., Nagiyev Sh. M. On the Rogers-Szegö polynomials. J. Phys. A Math. Gen. 27:1994;L661-L615.
11. Bressoud D. M. A simple proof of Mehler's formula forq. Indiana Univ. Math. J. 29:1980;577-580.
12. W. Y. C. Chen, Z. G. Liu, Parameter augmentation for basic hypergeometric series, I, Proc. Rotafest, Birkhäuser, Boston.
13. Chu W. C. Basic hypergeometric identities: An introductory revisiting through the Carlitz inversions. Forum Math. 7:1995;117-129.
14. Gasper G. q. Rassias T. M. Topics in Mathematical Analysis. 1989;294-314 World Scientific, Singapore.
15. Gasper G., Rahman M. Basic Hypergeometric Series. 1990;Cambridge Univ. Press, Cambridge.
16. Goldman J., Rota G.-C. The number of subspaces of a vector space. Tutte W. Recent Progress in Combinatorics. 1969;75-83 Academic Press, New York.
17. Goldman J., Rota G.-C. On the foundations of combinatorial theory. IV. Finite vector spaces and Eulerian generating functions. Stud. Appl. Math. 49:1970;239-258.
18. Ismail M. E. H., Stanton D. On the Askey-Wilson and Rogers polynomials. Canad. J. Math. 40:1988;1025-1045.
19. Ismail M. E. H., Stanton D., Viennot G. The combinatorics ofq. Europ. J. Combin. 8:1987;379-392.
20. Joichi J. T., Stanton D. Bijective proofs of basic hypergeomentric series identities. Pacific J. Math. 127:1987;103-120.
21. Kalnins E. G., Miller W. Symmetry techniques forq. Rocky Mountain J. Math. 19:1989;223-240.
22. Markett C. Linearization of the product of symmetric orthogonal polynomials. Constr. Approx. 10:1994;317-338.
23. Nassrallah B., Rahman R. Projection formulas, a reproducing kernel and a generating function forq. SIAM J. Math. Soc. 16:1985;211-229.
24. Paule P. On identities of the Rogers-Ramanujan type. J. Math. Anal. Appl. 107:1985;255-284.
25. Rahman M. A simple evaluation of Askey and Wilson'sq. Proc. Amer. Math. Soc. 92:1984;413-417.
26. Rahman M., Suslov S. K. Barnes and Ramanujan-Type integrals on theq. SIAM J. Math. Anal. 25:1994;1002-1022.
27. Rogers L. J. On a three-fold symmetry in the elements of Heine's series. Proc. London Math. Soc. 24:1893;171-179.
28. Rogers L. J. On the expansion of some infinite products. Proc. London Math. Soc. 24:1893;337-352.
29. Roman S. More on the umbral calculus, with Emphasis on theq. J. Math. Anal. Appl. 107:1985;222-254.
30. Roman S., Rota G.-C. The umbal calculus. Adv. in Math. 27:1978;95-188.
31. Rota G.-C. Finite Operator Calculus. 1975;Academic Press, New York.
32. Szegö G. Ein Beitrag zur Theorie der Theta funktionen. Sitz. Preuss. Akad. Wiss. Phus. Math. KL. 19:1926;242-252.
33. Szegö G. Orthogonal Polynomials. Amer. Math. Soc, Colloquium publications. 23:1975;American Math. Society, Providence.
34. Wilf H. S., Zeilberger. An algorithmic Proof theory for hypergeometric (ordinary and "q. Invent. Math. 108:1992;575-633.
35. Zeilberger D. Aqq. Europ. J. Combin. 8:1987;461-463.