20 citations · 61 across the 21 of their papers we have counts for
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A proof of the irrationality of motivated by nested radicals with roots of
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder Kumar Jagpal +1
In this work, we prove the irrationality of motivated by nested radicals with roots of of the kind and . Sample computations showing h…
Application of a new iterative formula for computing and nested radicals with roots of
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder Kumar Jagpal +1
In this work, we obtain an iterative formula that can be used for computing digits of and nested radicals of kind , where and $c_n = \sqrt{2…
Efficient application of the Voigt functions in the Fourier transform
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder K. Jagpal +1
In this work, we develop a method for rational approximation of the Fourier transform (FT) based on the real and imaginary parts of the complex error function \[ w(z) = e^{-z^2}(1…
A rational approximation of the two-term Machin-like formula for
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder Kumar Jagpal +1
In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of by using its rational approximation. In this appro…
An iterative method for computing by argument reduction of the tangent function
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder Kumar Jagpal +1
In this work, we develop a new iterative method for computing the digits of by argument reduction of the tangent function. This method combines a modified version of the iterat…
A generalized series expansion of the arctangent function based on the enhanced midpoint integration
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder K. Jagpal +1
In this work we derive a generalized series expansion of the acrtangent function by using the enhanced midpoint integration (EMI). Algorithmic implementation of the generalized ser…
A two-domain MATLAB implementation for efficient computation of the Voigt/complex error function
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder K. Jagpal +1
In this work we develop a new algorithm for the efficient computation of the Voigt/complex error function. In particular, in this approach we propose a two-domain scheme where the…
A method to reduce the Lehmer measure in a multi-term Machin-like formula for
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder K. Jagpal +1
Previously we have proposed a new method of transforming quotients into integer reciprocals in the Machin-like formulas for . As a further development, here we show how to gener…
A new form of the Machin-like formula for pi by iteration with increasing integers
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder K. Jagpal +1
We present a new form of the Machin-like formula for that can be generated by using iteration. This form of the Machin-like formula may be promising for computation of the cons…
Algorithmic determination of a large integer in the two-term Machin-like formula for pi
Sanjar M. Abrarov, Rajinder K. Jagpal, Rehan Siddiqui +1
In our earlier publication we have shown how to compute by iteration a rational number in the two-term Machin-like formula for pi of kind $$\fracπ{4}=2^{k-1}\arctan\lef…
Unconditional applicability of Lehmer's measure to the two-term Machin-like formula for
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder K. Jagpal +1
Lehmer defined a measure where the may be either integers or rational numbers in a Machin-like fo…
A single-domain implementation of the Voigt/complex error function by vectorized interpolation
S. M. Abrarov, B. M. Quine, R. Siddiqui +1
In this work we show how to perform a rapid computation of the Voigt/complex error over a single domain by vectorized interpolation. This approach enables us to cover the entire se…
Efficient application of the Chiarella and Reichel series approximation of the complex error function
S. M. Abrarov, B. M. Quine, R. K. Jagpal
Using the theorem of residues Chiarella and Reichel derived a series that can be represented in terms of the complex error function (CEF). Here we show a simple derivation of this…