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Euler's summation of the factorial series and a class of continued fractions

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Euler was the first mathematician to develop a systematic theory of divergent series, anticipating by over hundred years summation procedures of Abel, Borel, and others. This talk discusses a type of series that is summable by Borel’s method which in fact is what Euler did and obtained a continued fraction for its value. The continued fractions are not the usual ones and have interested many, including Ramanujan. The talk is based on joint work with Trond Digernes of Trondheim University.

This talk is part of the Number Theory Seminar series.

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