Similarly to what happened with the incomplete gamma function, we note that large values of v give worse results.
1 we illustrate the computation of the incomplete gamma function using the modified asymptotic series and the method of evaluation explained in Section 2.
As a general example, modified expansions for confluent hypergeometric functions are considered in Section 3, and as particular cases expansions for the incomplete gamma function [GAMMA](a, z) and the modified Bessel function [K.
Rudert, Tables of the Incomplete Gamma Function Ratio, Justus von Liebig Verlag, Darmstadt, Germany (1965).
Leon Harter, New Tables of the Incomplete Gamma Function Ratio and of Percentage Points of the Chi-Square and Beta Distributions, U.
In Equation (2), [Gamma] (a) is the gamma function, the integral is the incomplete gamma function denoted by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
In Figure 2, we depict the percentage error in the incomplete gamma function ratio P(a, z) = [Gamma](a, z)/ [Gamma](a) for values of a [Epsilon][1, 2] and values of z [Epsilon][0, 7].
where the incomplete Gamma function
is defined by [GAMMA](w,x) = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
He follows this with an illuminating treatment of models of human mortality, including the modeling of joint lifetimes and a technical note on the incomplete gamma function
1959, Some elementary inequalities relating to the Gamma and incomplete Gamma function
where all the input variables are now explicitly listed in the arguments of the ALDA function, and [GAMMA]F(x, y) denotes the incomplete Gamma function
Incomplete Gamma Functions
and Generalized Exponential Integral