Jonathan.Bradley-ThrushAffiliation: Title Of Talk: A classical method with applications to $q$-series
URLS: Abstract: In late-nineteenth-century work on the theory of elliptic functions, there is a particular method which is used to determine the Fourier series expansion of ratios of theta functions. I will describe this method with reference to Biehler's thesis of 1879, which contains several uses of it. I will then give some examples to show how the method may be applied to q-series, including a very short proof of the special case of Ramanujan's ${}_1\psi_1$ summation which is used to obtain formulae related to sums of squares. I will conclude by explaining how the method may be used to correct Askey's deliberately erroneous series expansion of a particular infinite product, which he gave as a cautionary example in his 1987 paper on formal Laurent series.
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Last update made Tue Mar 10 21:28:01 CDT 2026.
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