Algorithms for Calculating the Limits of Convergent Infinite Series

Year 2016, Volume: 4 Issue: 1, 175 - 182, 15.04.2016

Héctor Luna-garcía Luz María García-cruz Ana Elizabeth García

https://doi.org/10.36753/mathenot.421426

Abstract

We use algorithms to calculate the exact limits of a wide range of convergent infinite series by means of
special functions, these are polygamma functions.
However, in the case of alternating series, these algorithms do not allow the use of such functions, but
allow them to find the limits of this series. Finally, these methods are used as a powerful and simple tool
for calculating the limits of many infinite series as shown in the examples included.

Keywords

Convergent infinite series, Polygamma functions, Laplace transform

References

• [1] Arfken, G., Weber, H., and Harris, F., Mathematical Methods for Physicists: A Comprehensive Guide, Elsevier Academic Press, USA, 2012.
• [2] Spivak. M., Calculus, Editorial Reverté, España, 1992.
• [3] Abramowitz, M., Stegun, I., Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, Dover Publications, USA, 1964.
• [4] Gradshteyn, I., Ryzhik, I., Jeffrey, A., Zwillinger, D., Table of Integrals, Series and Products, Academic Press, USA, 2