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A new series for
$\pi$ via polynomial approximations to arctangent
Colleen M. Bouey, Herbert A. Medina and Erika Meza
Vol. 5 (2012), No. 4, 421–430
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Abstract |
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Using rational functions of the form we produce a family of efficient polynomial approximations to arctangent on the interval , and hence provide approximations to via the identity . We turn the approximations of into a series that gives about 21 more decimal digits of accuracy with each successive term. |
Keywords
polynomial approximations to arctangent, approximations of
$\pi$, series for $\pi$
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Mathematical Subject Classification 2010
Primary: 41A10
Secondary: 26D05
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Milestones
Received: 25 August 2011
Revised: 30 January 2012
Accepted: 4 March 2012
Published: 14 June 2013
Communicated by Kenneth S. Berenhaut
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Authors |
| Colleen M. Bouey | |
| Mathematics Department Loyola Marymount University 1 LMU Drive Los Angeles, CA 90045 United States |
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| Herbert A. Medina | |
| Mathematics Department Loyola Marymount University 1 LMU Drive Los Angeles, CA 90045 United States |
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| Erika Meza | |
| Mathematics Department Loyola Marymount University 1 LMU Drive Los Angeles, CA 90045 United States |
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