Tribasic integrals and identities of Rogers-Ramanujan type

Ismail, M.; Stanton, D.

doi:10.1090/S0002-9947-03-03338-5

Tribasic integrals and identities of Rogers-Ramanujan type
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by M. E. H. Ismail and D. Stanton PDF

Trans. Amer. Math. Soc. 355 (2003), 4061-4091 Request permission

Abstract:

Some integrals involving three bases are evaluated as infinite products using complex analysis. Many special cases of these integrals may be evaluated in another way to find infinite sum representations for these infinite products. The resulting identities are identities of Rogers-Ramanujan type. Some integer partition interpretations of these identities are given. Generalizations of the Rogers-Ramanujan type identities involving polynomials are given again as corollaries of integral evaluations.

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