Summary
The trapezoidal rule is applied to the numerical calculation of a known integral representation of the complementary incomplete gamma function Г (a,x) in the regiona<−1 andx>0. Since this application of the rule is not standard, a careful investigation of the remainder terms using the Euler-Maclaurin formula is carried out. The outcome is a simple numerical procedure for obtaining values of incomplete gamma functions with surprising accuracy in the stated region.
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This work has been supported by the Ministero della Pubblica Istruzione and the Consiglio Nazionale delle Ricerche
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Allasia, G., Besenghi, R. Numerical calculation of incomplete gamma functions by the trapezoidal rule. Numer. Math. 50, 419–428 (1986). https://doi.org/10.1007/BF01396662
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DOI: https://doi.org/10.1007/BF01396662