A matrix inverse
Author:
D. M. Bressoud
Journal:
Proc. Amer. Math. Soc. 88 (1983), 446-448
MSC:
Primary 33A30; Secondary 05A17
DOI:
https://doi.org/10.1090/S0002-9939-1983-0699411-9
MathSciNet review:
699411
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Abstract: George Andrews has demonstrated that the Bailey transform is equivalent to the inversion of an infinite-dimensional matrix whose entires are rational functions in $q$. We generalize this inversion by introducing an extra parameter which brings much greater symmetry.
- George E. Andrews, Connection coefficient problems and partitions, Relations between combinatorics and other parts of mathematics (Proc. Sympos. Pure Math., Ohio State Univ., Columbus, Ohio, 1978) Proc. Sympos. Pure Math., XXXIV, Amer. Math. Soc., Providence, R.I., 1979, pp. 1–24. MR 525316
- W. N. Bailey, Some identities in combinatory analysis, Proc. London Math. Soc. (2) 49 (1947), 421–425. MR 22816, DOI https://doi.org/10.1112/plms/s2-49.6.421
- W. N. Bailey, Identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (2) 50 (1948), 1–10. MR 25025, DOI https://doi.org/10.1112/plms/s2-50.1.1
- D. M. Bressoud, Some identities for terminating $q$-series, Math. Proc. Cambridge Philos. Soc. 89 (1981), no. 2, 211–223. MR 600238, DOI https://doi.org/10.1017/S0305004100058114
- Ira Gessel and Dennis Stanton, Applications of $q$-Lagrange inversion to basic hypergeometric series, Trans. Amer. Math. Soc. 277 (1983), no. 1, 173–201. MR 690047, DOI https://doi.org/10.1090/S0002-9947-1983-0690047-7
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Article copyright:
© Copyright 1983
American Mathematical Society
