Séminaire Lotharingien de Combinatoire, B44a (2000), 10 pp.
Mourad E. H. Ismail,
Helmut Prodinger, Dennis Stanton
Schur's Determinants and Partition Theorems
Abstract.
Garrett, Ismail, and Stanton gave a general formula that
contains the Rogers-Ramanujan identities as special
cases. The theory of associated orthogonal polynomials is then
used to explain determinants that Schur introduced in 1917 and show that the
Rogers-Ramanujan identities imply the Garrett, Ismail, and Stanton seemingly
more general formula. Using a result of Slater a continued
fraction is explicitly evaluated.
Received: April 30, 2000; Accepted: May 19, 2000.
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