Ramanujan's approximation to the exponential function and generalizations

Cormac O'Sullivan

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arXiv · 2205.08504

Ramanujan's approximation to the exponential function and generalizations

Cormac O'Sullivan

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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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Cormac O'Sullivan. 2022-05-17. Ramanujan's approximation to the exponential function and generalizations. https://arxiv.org/abs/2205.08504

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