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

REFERENCES

(1) sici

(2) sine integral

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

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