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The Gamma Function via Interpolation

04/01/2021

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by Matthew F Causley, et al.

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The Lanczos formula for the Gamma function is used in many software libraries due to its favorable convergence properties for complex argument. A simple proof that the formula interpolates the factorial function at the first few integers is given. A new interpolating formula is then proposed, which is more accurate, and attains a nearly uniform relative error.

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