Incomplete Exponential and Hypergeometric Functions with Applications to the Non Central χ²-Distribution

Abstract

Corresponding to the incomplete gamma functions,found useful in many problems,we propose incomplete exponential functions. Like the generalized incomplete gamma functions,the proposed functions have an additional parameter. It is shown that these functions can be related to Bessel functions. This leads us naturally to an incomplete extension of the hypergeometric function. The usefulness of these functions in some closed form representation of the non central χ²-distributions is demonstrated.

Key Words:

• Bessel functions
• Cumulative distribution function
• Generalized hypergeometric functions
• Incomplete gamma functions
• Non central χ²-distributions.

Mathematics Subject Classification:

• 33C05
• 33C15
• 33E99

Acknowledgment

The authors are grateful to the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for providing excellent research facilities through the Research Project MS/Zeta/242.