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Manuscript Title: Programs for computing the logarithm of the gamma function and the
digamma function for complex argument. | ||

Authors: K.S. Kolbig | ||

Program title: CLOGAM AND CDIGAM | ||

Catalogue identifier: ACRG_v1_0Distribution format: gz | ||

Journal reference: Comput. Phys. Commun. 4(1972)221 | ||

Programming language: Fortran. | ||

Computer: CDC 6600. | ||

Operating system: CDC SCOPE. | ||

RAM: 4K words | ||

Word size: 60 | ||

Keywords: General purpose, Nuclear physics, Atomic physics, Gamma function, Logarithm of gamma Function, Digamma function, Asymptotic expansion, Psi function, Phase shift, Schrodinger, Scattering. | ||

Classification: 4.7. | ||

Nature of problem:The gamma function, its logarithm, and its logarithmic derivative appear in a wide range of physical applications. We mention here only the Veneziano model and its generalizations in high-energy physics, and the Coulomb phase shift for complex energies. | ||

Solution method:For Re z>= 7, the asymptotic expansions are used to compute 1n gamma(z) and psi(z). For other regions of the z plane, suitable functional relations are used. Care is taken that Im 1n Gamma(z) is computed correctly, and not merely modulo 2 phi. | ||

Restrictions:As the tests show, an accuracy of 12-14 significant digits is normally obtained. | ||

Running time:Typical running times (in micro seconds on the CDC 6600) are given in table 1. Table 1 -------------------------------------------------------------------- 1n Gamma(z) (CLOGAM) psi(z) (CDIGAM) -------------------------------------------------------------------- Re z < -6 580 570 -6<= Re z < 0 790 650 0<= Re z < 7 630 390 7<= Re z 330 300 -------------------------------------------------------------------- |

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