In the relativistic Doppler effect, gamma equals one divided by the square root of one minus beta squared: γ = 1/√(1 − β²). Here, β is the relative speed divided by the speed of light, v/c.
The symbol γ is the Lorentz factor, introduced through special relativity to describe how measurements of time, length, and frequency change between inertial observers. As β approaches 1, meaning the relative speed approaches light speed, γ grows rapidly. At ordinary speeds, β is tiny and γ is very close to 1, so relativistic effects are negligible.
This gamma factor modifies the classical Doppler effect for light. The full relativistic treatment combines the familiar frequency change caused by motion with time dilation and does not require a material medium, unlike sound. A common mix-up is confusing β with gamma itself: β measures speed as a fraction of c, while γ is calculated from β. The related formula also appears in time dilation and length contraction.