TL;DR
This paper extends the use of the Trapezoidal Rule to efficiently evaluate various special functions like Incomplete Gamma and Confluent Hypergeometric functions through integral representations.
Contribution
It introduces a generalized approach for applying the Trapezoidal Rule to a broader class of special functions in mathematical physics.
Findings
Effective approximation of Incomplete Gamma functions
Efficient evaluation of Confluent Hypergeometric functions
Extension of trapezoidal rule techniques to new functions
Abstract
We extend the technique of using the Trapezoidal Rule for efficient evaluation of the Special Functions of Mathematical Physics given by integral representations. This technique was recently used for Bessel functions, and here we treat Incomplete Gamma functions and the general Confluent Hypergeometric Function.
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