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Updated: Sep 16, 2025

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
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Global approximation to the Boys functions for vectorized computation.

Dimitri N Laikov1

  • 1Chemistry Department, Moscow State University, 119991 Moscow, Russia.

The Journal of Chemical Physics
|July 8, 2025
PubMed
Summary
This summary is machine-generated.

A new analytical expression provides a fast approximation for Boys functions, essential for calculations involving the lower incomplete gamma function. This efficient method simplifies complex computations for broader scientific applications.

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Area of Science:

  • Mathematical Physics
  • Computational Chemistry

Background:

  • Boys functions are crucial in various scientific fields, including quantum chemistry.
  • Existing methods for calculating Boys functions can be computationally intensive.
  • Accurate and efficient approximations are needed for large-scale simulations.

Purpose of the Study:

  • To develop a fast, closed-form analytical approximation for Boys functions.
  • To ensure the approximation is valid for all argument values.
  • To create a computationally efficient method suitable for vectorization.

Main Methods:

  • Developed a single closed-form analytical expression for Boys functions.
  • The approximation utilizes basic arithmetic operations and square roots.
  • Tested the accuracy and performance of the developed expression.

Main Results:

  • A fast approximation for Boys functions has been successfully developed and validated.
  • The expression requires minimal computational operations beyond the exponential function.
  • The method is straightforward to implement in vectorized computations.

Conclusions:

  • The new analytical approximation offers a significant computational advantage for Boys functions.
  • This method simplifies calculations related to the lower incomplete gamma function.
  • The efficiency makes it suitable for demanding computational tasks in science and engineering.