A comparison of the Maclaurin and Chebyshev series in the computation of tan-1x

• Main Authors: Castro, Elizabeth, Lim, Marsha
• Format: text
• Language: English
• Published: Animo Repository 1993
• Subjects: Series, Taylor's; Chebyshev approximation; Mathematics > Formulae; Programming (Mathematics); Maclaurin's series (Mathematics)
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16108
• Institution: De La Salle University

This thesis presents a comparison of the MacLaurin and Chebyshev series in the computation of tan -1x in terms of the simplicity of the process of computation and the number of terms needed to achieve the desired level of accuracy.The power series expansion of the inverse tangent function usually gives an accurate estimate. However, for values of x close to 1 or -1, the series converges slowly.In the article Some Formulae for Calculating Tan -1x found in Mathematics Gazette, R.E. Scraton presents a formula for taking iterates of x using either the Maclaurin or Chebyshev series. S considerably less number of terms is needed for the calculation to give an accurate value.The results of the comparison indicate that in terms of the computation, the Maclaurin series is simpler to apply. However, less number of terms is needed to achieve the desired level of accuracy using the Chebyshev series.