Computing the Incomplete Gamma Function to Arbitrary Precision
نویسنده
چکیده
I consider an arbitrary-precision computation of the incomplete Gamma function from the Legendre continued fraction. Using the method of generating functions, I compute the convergence rate of the continued fraction and find a direct estimate of the necessary number of terms. This allows to compare the performance of the continued fraction and of the power series methods. As an application, I show that the incomplete Gamma function Γ (a, z) can be computed to P digits in at most O (P ) long multiplications uniformly in z for Re z > 0. The error function of the real argument, erfx, requires at most O(P ) long multiplications.
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