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Ramanujan's approximation to the exponential function and generalizations (2205.08504v1)
Published 17 May 2022 in math.NT and math.CO
Abstract: Ramanujan's approximation to the exponential function is reexamined with the help of Perron's saddle-point method. This allows for a wide generalization that includes the results of Buckholtz, and where all the asymptotic expansion coefficients may be given in closed form. Ramanujan's approximation to the exponential integral is treated similarly.
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