TL;DR
This paper introduces a new numerical method using the Trapezoidal Rule applied to integral representations for accurately computing Bessel functions on modern computers.
Contribution
It proposes a simple, accurate, and flexible computational procedure for evaluating Bessel functions, potentially improving existing methods for special functions.
Findings
The Trapezoidal Rule is effective for Bessel function evaluation.
The method offers simplicity and accuracy for numerical computations.
It enhances computational approaches for special functions in mathematical physics.
Abstract
A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The Trapezoidal Rule, applied to suitable integral representations, may become the method of choice for evaluation of the many Special Functions of mathematical physics.
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