Students of mathematical physics, engineering, natural and biological sciences sometimes need to use special functions that are not found in ordinary mathematical software. In this paper a simple universal numerical algorithm is developed to compute the Legendre function values of the first kind using the Legendre differential equation. The computed function values are compared to built-in values in Mathcad14 and Derive6. Error analysis is performed to test the accuracy of the algorithm. Graphical residuals are found to be of order 10-12. Finally, some physical application is presented
Reference:
Motsepe, K, Fedotov, I, Shatalov, M and Joubert, SV. 2008. Numerical computation of special functions with applications to physics. Technology and its Integration into Mathematics Education Conference (TIME). Buffelspoort, South Africa, 22 - 26 September 2008, pp 153-161
Motsepe, K., Fedotov, I., Shatalov, M., & Joubert, S. (2008). Numerical computation of special functions with applications to physics. Buffelspoort TIME2008 Peer-reviewed Conference Proceedings. http://hdl.handle.net/10204/3245
Motsepe, K, I Fedotov, M Shatalov, and SV Joubert. "Numerical computation of special functions with applications to physics." (2008): http://hdl.handle.net/10204/3245
Motsepe K, Fedotov I, Shatalov M, Joubert S, Numerical computation of special functions with applications to physics; Buffelspoort TIME2008 Peer-reviewed Conference Proceedings; 2008. http://hdl.handle.net/10204/3245 .
