TeXipedia

varpi

Represents a variant form of the lowercase Greek letter pi, providing a stylistic alternative in mathematical notation.

Overview

Serves as a distinct visual variant of pi (π) in mathematical contexts where multiple pi-like symbols are needed to represent different quantities or variables.

  • Commonly used in advanced mathematics and theoretical physics when regular pi is already assigned to another meaning.
  • Particularly useful in equations requiring multiple distinct pi-like symbols to avoid confusion.
  • Often appears in specialized mathematical notation where visual distinction between similar symbols is crucial.

Examples

Using varpi as a parameter in a wave function equation.

ψ(x,t)=Aei(kx−ϖt)\psi(x,t) = A e^{i(kx - \varpi t)} 
\psi(x,t) = A e^{i(kx - \varpi t)}

Representing angular frequency in a harmonic oscillator equation.

x¨+ϖ2x=0\ddot{x} + \varpi^2 x = 0 
\ddot{x} + \varpi^2 x = 0

Defining the natural frequency in a resonance formula.

R(ω)=1(ϖ02−ω2)2R(\omega) = \frac{1}{\sqrt{(\varpi_0^2 - \omega^2)^2}} 
R(\omega) = \frac{1}{\sqrt{(\varpi_0^2 - \omega^2)^2}}