The Mathematical Institute, University of Oxford, Eprints Archive

Computing the Gamma function using contour integrals and rational approximations

Schmelzer, Thomas and Trefethen, Lloyd N. (2005) Computing the Gamma function using contour integrals and rational approximations. Technical Report. Unspecified. (Submitted)

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Abstract

Some of the best methods for computing the gamma function are based on numerical evaluation of Hankel's contour integral. For example, Temme evaluates this integral based on steepest-decent contours by the trapezoid rule. Here we investigate a different approach to the integral: the application of the trapezoid rule on Talbot-type contours using optimal parameters recently derived by Weideman for computing inverse Laplace transforms. Relatedly, we also investigate quadrature formulas derived from best approximations to exp(z) on the negative real axis, following Cody, Meinardus and Varga. The two methods are closely related and both converge geometrically. We find that the new methods are competitive with existing ones, even though they are based on generic tools rather than on specific analysis of the gamma function.

Item Type:Technical Report (Technical Report)
Subjects:O - Z > Special functions
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1126
Deposited By:Lotti Ekert
Deposited On:12 May 2011 08:37
Last Modified:12 May 2011 08:37

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