The directivity of the dipole antenna is given be the expression:
<math> D_0 \approx \frac{2 \left[ \frac{\text{cos} \left( \frac{k_0 L}{2} \text{cos} \theta \right) - \text{cos} \left( \frac{k_0 L}{2} \right) }{\text{sin}\theta} \right]^2 } {C + \text{ln}(k_0L) - C_i(k_0L) + \frac{1}{2} \text{sin}(k_0L) \left[ S_i(2k_0L) - 2S_i(k_0L) \right] + \frac{1}{2} \text{cos}(k_0L) \left[ C + \text{ln}(k_0L/2) + C_i(2k_0L) - 2C_i(k_0L) \right] } </math> where C = 0.5772 is Euler's constant, and C<sub>i</sub>(x) and S<sub>i</sub>(x) are the cosine and sine integrals, respectively:Â <math> C_i(x) = - \int_{x}^{\infin} \frac{ \text{cos} \tau}{\tau} d\tau </math>Â <math> S_i(x) = \int_{0}^{x} \frac{ \text{sin} \tau}{\tau} d\tau </math>
=== A Note on the Rotation of Antenna Radiation Patterns ===