27 citations · 236 across the 52 of their papers we have counts for
4 papers · 2 filters
An iteration procedure for a two-term Machin-like formula for pi with small Lehmer's measure
S. M. Abrarov, B. M. Quine
In this paper we present a two-term Machin-like formula for pi \[\fracπ{4} = 2^{k - 1}\arctan\left(\frac{1}{u_1}\right) + \arctan\left(\frac{1}{u_2}\right)\] with small Lehmer's me…
The two-term Machin-like formula for pi with small arguments of the arctangent function
S. M. Abrarov, B. M. Quine
In this paper we propose a new method for determination of the two-term Machin-like formula for pi with arbitrarily small arguments of the arctangent function. This approach exclud…
A set of the Viète-like recurrence relations for the unity constant
S. M. Abrarov, B. M. Quine
Using a simple Viète-like formula for based on the nested radicals and , we derive a set of the recurrence relations for the constant…
A reformulated series expansion of the arctangent function
S. M. Abrarov, B. M. Quine
In our recent publication we obtained a series expansion of the arctangent function involving complex numbers. In this work we show that this formula can also be expressed as a rea…