M.S. (Master of Science)
Department of Mathematical Sciences
One of the most famous results from q-series is that of the Rogers-Ramanujan continued fraction, given by [special characters omitted]. G.E. Andrews and D. Bowman gave a full extension of this continued fraction using G.N. Watson’s nonterminating very well-poised 8φ7 function. As opposed to Ramanujan’s generalization that only used four variables, this generalization is given in seven variables, and certain q-series identities naturally arise from it. As a special case of their theorem, Andrews and Bowman gave the following identity: [special characters omitted]. This thesis will give a full proof of Andrews and Bowman’s result, as well as investigate other special cases of their continued fraction that have not been discovered before. Many identities will be verified using an open-source symbolic algebra package called Maxima.
Zollinger, Bryan Thomas, "Some Special Cases of the andrews-Bowman Continued Fraction" (2021). Graduate Research Theses & Dissertations. 7810.
Northern Illinois University
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