Cn and Dn very-well-poised 10φ9 transformations

Constructive Approximation

Volumn 14, Issue 4, 1998, Pages 531-567

  Bhatnagar, G ^a,b   Schlosser, M ^c  

^a OHIO STATE UNIVERSITY   (United States)

^b R and D NIIT Ltd   (India)

^c UNIVERSITY OF VIENNA   (Austria)

Author keywords

Jackson's 8 7 summations; Multiple basic hypergeometric series associated to root systems An, Cn, and Dn; Sears' 4 3 transformations; Terminating 10 9 transformations; Watson's transformations

Indexed keywords

EID: 0040532143     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003659900089     Document Type: Article

References (38)

1. G. E. ANDREWS (1976): The Theory of Partitions, vol. 2 (G.-C. Rota, ed.). Encyclopedia of Mathematics and Its Applications. Reading, MA: Addison-Wesley.
2. G. E. ANDREWS (1975): Problems and prospects for basic hypergeometric series. In: Theory and Application of Special Functions (R. Askey, ed.). New York: Academic Press, pp. 191-224.
3. W. N. BAILEY (1935): Generalized Hypergeometric Series. Cambridge: Cambridge University Press. Reprinted by Stechert-Hafner, New York, 1964.
4. W. N. BAILEY (1929): An identity involving Heine's basic hypergeometric series. J. London Math. Soc., 4:254-257.
5. W. N. BAILEY (1947): Some identities in combinatory analysis. Proc. London Math. Soc., 49:421-435.
6. G. BHATNAGAR (1995): Inverse Relations, Generalized Bibasic Series and Their U (n) Extensions. Ph.D. thesis, Ohio State University.
7. n Basic Hypergeometric Series.
8. re série. T VIII, Paris: Gauthier-Villars, 1893, pp. 42-50.
9. re série. T VIII, Paris: Gauthier-Villars, 1893, pp. 42-50.
10. S. DEGENHARDT, S. C. MILNE (in preparation): A nonterminating q-Dougall summation theorem for basic hypergeometric series in U (n).
11. R. Y. DENIS, R. A. GUSTAFSON (1992): An SU (n) q-beta integral transformation and multiple hypergeometric series identities. SIAM J. Math. Anal., 23:552-561.
12. G. GASPER, M. RAHMAN (1990): Basic Hypergeometric Series. Encyclopedia of Mathematics and Its Applications, vol. 35. Cambridge: Cambridge University Press.
13. R. A. GUSTAFSON (1987): A Whipple's transformation for hypergeometric series in U (n) and multivariable orthogonal polynomials. SIAM J. Math. Anal., 18:495-530.
14. R. A. GUSTAFSON (1989): The Macdonald identities for affine root systems of classical type and hypergeometric series very well-poised on semi-simple Lie algebras. In: Ramanujan International Symposium on Analysis (Dec. 26th to 28th, 1987, Pune, India) (N. K. Thakare, ed.), pp. 187-224.
15. E. HEINE (1846): Untersuchungen über die Reihe . . . . J. Reine Angew. Math., 34:285-328.
16. W. J. HOLMAN III, L. C. BIEDENHARN, J. D. LOUCK (1976): On hypergeometric series well-poised in SU (n). SIAM J. Math. Anal., 7:529-541.
17. F. H. JACKSON (1910): Transformations of q-series. Messenger of Math., 39:145-153.
18. F. H. JACKSON (1921): Summation of q-hypergeometric series. Messenger of Math., 57:101-112.
19. C. G. J. JACOBI (1881): Fundamenta nova theoriae functionum ellipticarum. 1829 Regiomnoti, fratrum Bornträger. Reprinted in Gesammelte Werke, vol. 1. Berlin: Reimer, pp. 49-239.
20. n2-1∞ and Basic Hypergeometric Series in U (n).
21. l. Adv. in Math., 57:34-70.
22. S. C. MILNE (1988): Multiple q-series and U (n) generalizations of Ramanujan's 1ψ1 sum. In: Ramanujan Revisited (G. E. Andrews et al., eds.). New York: Academic Press, pp. 473-524.
23. S. C. MILNE (1994): A q-analog of a Whipple's transformation for hypergeometric series in U (n). Adv. in Math., 108:1-76.
24. S. C. MILNE (1997): Balanced 3φ2 summation theorems for U (n) basic hypergeometric series. Adv. in Math., 131:93-187.
25. S. C. MILNE (in preparation): New Whipple's transformations for basic hypergeometric series in U (n).
26. 1 Bailey transform and Bailey lemma. Discrete Math., 139:319-346.
27. S. C. MILNE, J. W. NEWCOMB (1996): U (n) very well poised 10φ9 transformations. J. Comput. Appl. Math., 68:239-285.
28. S. C. MILNE, J. W. NEWCOMB (in preparation): Nonterminating q-Whipple transformations for basic hypergeometric series in U (n).
29. J. W. NEWCOMB (1993): The Classical U (n) Bailey Transform and 10φ9 Transformations. Ph.D. Thesis. University of Kentucky.
30. r basic hypergeometric series. Ramanujan J., 1: 243-274.
31. M. SCHLOSSER (1996): Multidimensional Matrix Inversions and Multiple Basic Hypergeometric Series. Ph.D. Thesis. Universität Wien.
32. M. SCHLOSSER (preprint): Summation Theorems for Multidimensional Basic Hypergeometric Series by Determinant Evaluations.
33. D. B. SEARS (1951): On the transformation theory of basic hypergeometric functions. Proc. London Math. Soc., (2) 53:158-180.
34. L. J. SLATER (1966): Generalized Hypergeometric Functions. London: Cambridge University Press.
35. D. STANTON (1989): An elementary approach to the Macdonald identities. In: q-Series and Partitions (D. Stanton, ed.). IMA Volumes in Mathematics and Its Applications, vol. 18. New York: Springer-Verlag, pp. 139-150.
36. G. N. WATSON (1929): A new proof of the Rogers-Ramanujan identities. J. London Math. Soc., 4:4-9.
37. F. J. W. WHIPPLE (1926): On well-poised series, generalized hypergeometric series having parameters in pairs, each pair with the same sum. Proc. London Math. Soc., 24:247-263.
38. F. J. W. WHIPPLE (1926): A fundamental relation between generalized hypergeometric series. J. London Math. Soc., 1:138-145.