1.1 q -binomial coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 1.2 Unimodality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 1.3 Congruences for the partition function . . . . . . . . . . . . . . . . . . . . . . . . . 143 1.4 The Jacobi triple product identity . . . . . . . . . . . . . . . . . ...

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...

New short and easy computer proofs of finite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the first Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping. AMS Subject Classification. 05A19; secondary 11B65, 05A17

New short and easy computer proofs of nite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the rst Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping.