20 citations · 61 across the 21 of their papers we have counts for
21 papers
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…
Rapid computation of the total band radiance by using the Spectrally Integrated Voigt Function
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder K. Jagpal +1
In our earlier publication we introduced the Spectrally Integrated Voigt Function (SIVF) as an alternative to the traditional Voigt function for the HITRAN-based applications [Quin…
Effect of the instrument slit function on upwelling radiance from a wavelength dependent surface reflectance
Rajinder K. Jagpal, Rehan Siddiqui, Sanjar M. Abrarov +1
The Radiance Enhancement (RE) method was introduced for efficient detection of clouds from the space. Recently, we have also reported that due to high reflectance of combustion-ori…
Efficient application of the Radiance Enhancement method for detection of the forest fires due to combustion-originated reflectance
Rehan Siddiqui, Rajinder K. Jagpal, Sanjar M. Abrarov +1
The existing methods for detection of the cloud scenes are applied at relatively small spectral range within shortwave upwelling radiative wavelength flux. We have reported a new m…
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…
Carbon dioxide retrieval of Argus 1000 space data by using GENSPECT line-by-line radiative transfer model
R. K. Jagpal, R. Siddiqui, S. M. Abrarov +1
The micro-spectrometer Argus 1000 being in space continuously monitors the sources and sinks of the trace gases. It is commonly believed that among other gases …
Radiance Enhancement and Shortwave upwelling Radiative Flux methods for efficient detection of cloud scenes
Rehan Siddiqui, Rajinder K. Jagpal, Sanjar M. Abrarov +1
The description, imagery and interpretation of cloud scenes by remote sensing datasets from Earth-orbiting satellites have become a great debate for several decades. Presently, the…
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…
A sampling-based approximation of the complex error function and its implementation without poles
S. M. Abrarov, B. M. Quine, R. K. Jagpal
Recently we developed a new sampling methodology based on incomplete cosine expansion of the sinc function and applied it in numerical integration in order to obtain a rational app…
Short Wave upwelling Radiative Flux (SWupRF) within NIR range for the selected greenhouse wavelength bands of O2, H2O, CO2 and CH4 by Argus 1000 along with GENSPECT line by line radiative transfer model
Rehan Siddiqui, Rajinder Jagpal, Naif Al Salem +1
This new study develops an algorithm for Short Wave upwelling Radiative Flux (SWupRF) for the spectral variations within near infrared (NIR) from 1100 to 1700 nm wavelength band ba…
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…
On the Equivalence of Fourier Expansion and Poisson Summation Formula for the Series Approximation of the Exponential Function
S. M. Abrarov, B. M. Quine, R. K. Jagpal
In this short note we show the equivalence of Fourier expansion and Poisson summation approaches for the series approximation of the exponential function . The a…