The title Gregory's series has the form arctan x = x - x 3 3 + x 5 5 - x 7 7 + ⋯ and was discovered in 1671 by Scottish mathematician James Gregory. This ...
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In this paper the countable family of generalized Gregory's series (all of which are the power series having the radius of convergence equal to one) is defined.
The title Gregory's series has the form(1) arctan x = x - x 3 3 + x 5 5 - x 7 7 + ⋯ and was discovered in 1671 by Scottish mathematician James Gregory. This ...
The series representing the generalizations of classical James Gregory's series are discussed in this paper. Formulae describing sums of these series are found.
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The Gregory series is a pi formula found by Gregory and Leibniz and obtained by plugging x=1 into the Leibniz series.
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Gregory coefficients are alternating G n = (−1) n−1 |G n | for n > 0 and decreasing in absolute value. These numbers are named after James Gregory.
Oct 22, 2024 · The series representing the generalizations of classical James Gregory's series are discussed in this paper. Formulae describing sums of these series are found.
SOME GENERALIZATIONS OF GREGORY'S POWER SERIES AND THEIR APPLICATIONS · Mathematics · 2013. The series representing the generalizations of classical James ...
Oct 22, 2024 · In this paper the countable family of generalized Gregory's series (all of which are the power series having the radius of convergence equal ...
A non-traditional proof of the Gregory-Leibniz series, based on the relationships among the zeta function, Bernoulli coefficients, and the. Laurent expansion of ...