Incomplete Bessel, generalized incomplete gamma, or leaky aquifer functions

On an Extension of Generalized Incomplete Gamma Functions with Applications

In this paper we have introduced extensions yv(a, x; b) and fu(a, x; b) of the generalized Gamma functions y (a, x; b) and V(a, x\ b) considered recently by Chaudhry and Zubair. These extensions are found useful in the representations of the Laplace and tf-transforms of a class of functions. We have also defined a generalization of the inverse Gaussian distribution. The cumulative and the relia...

Asymptotics of the modified bessel and the incomplete gamma matrix functions

h thii paper, an asymptotic expression of the incomplete gamma matrix function and integral expressions of Bessel matrix functions are given. Results are applied to study the asymptotic behavior of the modified Bessel function. @ 2003 Elsevier Science Ltd. All rights reserved. Keywords-Bessel function, Incomplete gamma function, Asymptotics.

Monotonicity of Ratios Involving Incomplete Gamma Functions with Actuarial Applications

Ratios involving incomplete gamma functions and their monotonicity properties play important roles in financial risk analysis. We derive desired monotonicity properties either using Pinelis’ Calculus Rules or applying probabilistic techniques. As a consequence, we obtain several inequalities involving conditional expectations that have been of interest in actuarial science.

A uniform asymptotic expansion for the incomplete gamma functions revisited

A new uniform asymptotic expansion for the incomplete gamma function Γ(a, z) valid for large values of z was given by the author in J. Comput. Appl. Math. 148 (2002) 323–339. This expansion contains a complementary error function of an argument measuring transition across the point z = a, with easily computable coefficients that do not involve a removable singularity in the neighbourhood of thi...

Certain Incomplete Numerical Functions*