Friday, November 27, 2009

SINE INTEGRAL IN SCIPY

THE SINE INTEGRAL

The Sine Integral is a very important function in Physics, Astronomy, Electrodynamics, Mathematical Physics,Optics and Signal Processing.

A fundamental result in the sine integral is;

This result is analytically proven using contour integrals concept from complex theory.


TRYING IT IN MATLAB



MATLAB gives excellent results, particularly for the special case of (0-inf )it gives correct value.

TRYING IT IN SCIPY


In Scipy the sine integral (and the cosine integral) is via (si,ci) = sici function. It yields excellent values for numbers, however for infinity it yields nan (not a number). This should probably be corrected with an exception in the sici module.

It is worth noting that for sufficiently high values (which tend to infinity) the desired result of 1.57.... ( = pi/2) is obtained, which confirms the numerical evaluation is correct


REFERENCES

(1)
sici
(2) sine integral




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