Bowman, Douglas, 1965-
Ph.D. (Doctor of Philosophy)
Department of Mathematical Sciences
This dissertation studies the method of iteration introduced by Nathan J. Fine for the function [Special characters omitted], where q is a fixed complex number with |q| < 1, |t| < 1 and (z)[sub n] = (1 - z)(1 - zq)(1 - zq²)...(1 - zq^(n-1)) for n < 0 and (z)₀ = 1 (for z [element of] C). Generalizing Fine's methods yields new basic hypergeometric identities. Certain identities have partition theory interpretations and are proved combinatorially using the method of overpartitions. Among other basic hypergeometric identities, generalizations of the Rogers-Fine identity are given.
Wesley, Sarah, "Variants of Fine transformations" (2018). Graduate Research Theses & Dissertations. 6631.
Northern Illinois University
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