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Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials

1961
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Mathematics of Computation
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During the course of some work on the diffraction theory of aberrations it was necessary to evaluate numerically the incomplete gamma function of imaginary argument y(v, ix) for certain values of the parameter v. These integrals are special cases of the confluent hypergeometric function, and in the standard notation [1] .ix y(v, ix) = / e~'t' ' dt 7?e(") > 0 (1) Jo where XFX is the confluent hypergeometric function. Only the case of v real is considered. When v is an integer, iFi is simply a

doi:10.1090/s0025-5718-1961-0128058-1
fatcat:6r55yzufcrbvfghlwtehcg35qy