CosIntegral

CosIntegral (z)

The CosIntegral(z) function returns the cosine integral of z.

If z is real, a real value is returned. If z is complex then a complex value is returned.

The CosIntegral function was added in Igor Pro 7.00.

Details

The cosine integral is defined by

$$\displaystyle \operatorname{Ci}(z)=\gamma+\ln (z)+\int_{0}^{z} \frac{\cos (t)-1}{t} d t, \quad(|\arg (z)|<\pi)$$

where γ is the Euler-Mascheroni constant 0.5772156649015328606065.

IGOR computes the cosine integral using the expression:

$$\displaystyle \operatorname{Ci}(z)=-\frac{Z^{2}}{4}{ }_{2} F_{3}\left(1,1 ; 2,2, \frac{3}{2} ;-\frac{z^{2}}{4}\right)+\ln (z)+\gamma,$$

References

Abramowitz, M., and I.A. Stegun, "Handbook of Mathematical Functions", Dover, New York, 1972. Chapter 5.

See Also

SinIntegral, ExpIntegralE1, HyperGPFQ