<math> E_\phi(\theta,\phi) \approx 0 </math>
where k<sub>0</sub> = 2π/λ<sub>0</sub> is the free-space wavenumber, λ<sub>0</sub> is the free-space wavelength, η<sub>0</sub> = 120π Ω is the free=-space intrinsic impedance, I<sub>0</sub> is the current on the dipole, and L is the length of the dipole.
The directivity of the dipole antenna is given be the expression:
where γ = 0.5772 is the Euler-Mascheroni 's constant, and C<sub>i</sub>(x) and S<sub>i</sub>(x) are the cosine and sine integrals, respectively:
<math> S_i(x) = \int_{0}^{x} \frac{ \text{sin} \tau}{\tau} d\tau </math>
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In the case of a half-wave dipole, L = λ<sub>0</sub>/2, and D<sub>0</sub> = 1.643.
=== A Note on the Rotation of Antenna Radiation Patterns ===