Research and Advances

Complex gamma function with error control

An algorithm to compute the gamma function and the loggamma function of a complex variable is presented. The standard algorithm is modified in several respects to insure the continuity of the function value and to reduce accumulation of round-off errors. In addition to computation of function values, this algorithm includes an object-time estimation of round-off errors. Experimental data with regard to the effectiveness of this error control are presented. A Fortran program for the algorithm appears in the algorithms section of this issue.

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Research and Advances

Algorithm 421: complex gamma function with error control [S14]

This Fortran program computes either the gamma function or the loggamma function of a complex variable in double precision. In addition, it provides an error estimate of the computed answer. The calling sequences are: CALL CDLGAM (Z, W, E, 0) for the loggamma, and CALL CDLGAM (Z, W, E, 1) for the gamma, where Z is the double precision complex argument, W is the answer of the same type, and E is a single precision real variable. Before the call, the value of E is an estimate of the error in Z, and after the call, it is an estimate of the error in W.

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