24 citations · 31 across the 5 of their papers we have counts for
8 papers
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…
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 simple identity for derivatives of the arctangent function
S. M. Abrarov, B. M. Quine
We present an identity for the derivatives of the arctangent function as an alternative to the Adegoke - Layeni - Lampret formula. We show that algorithmic implementation of the pr…
A rational approximation of the arctangent function and a new approach in computing pi
S. M. Abrarov, B. M. Quine
We have shown recently that integration of the error function represented in form of a sum of the Gaussian functions provides an asymptotic expansion s…
A new asymptotic expansion series for the constant pi
S. M. Abrarov, B. M. Quine
In our recent publications we have introduced the incomplete cosine expansion of the sinc function for efficient application in sampling [Abrarov & Quine, Appl. Math. Comput., 258…
A rational approximation for efficient computation of the Voigt function in quantitative spectroscopy
S. M. Abrarov, B. M. Quine
We present a rational approximation for rapid and accurate computation of the Voigt function, obtained by residue calculus. The computational test reveals that with only summa…