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We have shown recently that integration of the error function erf (x) represented in form of a sum of the Gaussian functions provides an asymptotic expansion series for the constant pi. In this work we derive a rational approximation of the arctangent function and make a conjecture for −sgn (x) π/2 + arctan (x), where sgn (x) is the signum function. The(More)
In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified representation of the proposed complex error function approximation makes possible further algorithmic optimization resulting in a(More)
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