A proof of the Gregory-Leibniz series and new series for calculating pi
Frank W. K. Firk
TL;DR
This paper presents a novel proof of the Gregory-Leibniz series using advanced mathematical functions and derives new series formulas for calculating pi, enhancing understanding and computational methods.
Contribution
It introduces a non-traditional proof of the Gregory-Leibniz series and derives new series formulas for pi based on zeta functions and Bernoulli coefficients.
Findings
New proof of the Gregory-Leibniz series
Derivation of new series for pi calculation
Connections among zeta function, Bernoulli coefficients, and cotangent expansion
Abstract
A non-traditional proof of the Gregory-Leibniz series, based on the relationships among the zeta function, Bernoulli coefficients, and the Laurent expansion of the cotangent is given. New series for calculating pi are obtained.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Mathematical Identities · Quantum Mechanics and Applications