A fast algorithm for computing the Boys function

Area of Science:

• Computational physics
• Numerical analysis

Background:

• The Boys function is crucial in various physics and chemistry calculations.
• Existing algorithms for computing the Boys function can be computationally intensive.

Purpose of the Study:

• To develop a novel, fast algorithm for computing the Boys function.
• To provide an efficient method for evaluating the Boys function with both real and complex arguments.

Main Methods:

• The study introduces a new algorithm based on a nonlinear approximation of the Boys function's integrand.
• The approximation utilizes exponential functions for enhanced computational speed.
• The algorithm is designed to handle both real and complex-valued arguments.

Main Results:

• The developed algorithm demonstrates significant speed improvements for Boys function computation.
• The algorithm achieves accuracy competitive with established methods.
• It successfully evaluates the Boys function across real and complex domains.

Conclusions:

• The new algorithm offers an efficient and accurate alternative for Boys function computation.
• This advancement has implications for accelerating calculations in fields relying on the Boys function.