New BBP-Type Formulae for π Derived from New Forms of Taylor Expansions of Inverse Tangent Function

Xin Wu, Zhongfan Chen and Yinan Zhu
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Xin Wu: School of Civil Engineering, Southeast University, Nanjing 211189, China
Zhongfan Chen: School of Civil Engineering, Southeast University, Nanjing 211189, China
Yinan Zhu: School of Civil Engineering, Southeast University, Nanjing 211189, China

Mathematics, 2022, vol. 10, issue 3, 1-15

Abstract: In this work, we give two new Taylor expansions of arctan( x + ω), where ω represents a finite increment of x . We discover several remarkable infinite series from these expansions by special substitutions. Some of these infinite series give BBP-type formulae.

Keywords: BBP-type formula; Taylor expansion; infinite series (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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