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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