TeXipedia

Phi

Represents a capital Greek letter commonly used in mathematics, physics, and statistics to denote various quantities and functions.

Overview

A versatile symbol that appears frequently across multiple scientific disciplines and mathematical contexts.

  • Often used to represent cumulative distribution functions in probability and statistics
  • Common in physics for electric flux, magnetic flux, and potential functions
  • Appears in engineering for phase angles and transfer functions
  • Used in geometry and topology to denote mappings and transformations
  • Distinct from the lowercase phi (φ), though both are used in related contexts

Examples

Using the capital Phi symbol to represent a cumulative distribution function in probability theory.

P(Xx)=Φ(xμσ)P(X \leq x) = \Phi\left(\frac{x-\mu}{\sigma}\right)
P(X \leq x) = \Phi\left(\frac{x-\mu}{\sigma}\right)

Representing magnetic flux in physics equations.

ΦB=SBdA\Phi_B = \oint_S \vec{B} \cdot d\vec{A}
\Phi_B = \oint_S \vec{B} \cdot d\vec{A}

Denoting a potential function in classical mechanics.

Φ(r)=GMr\Phi(r) = -\frac{GM}{r}
\Phi(r) = -\frac{GM}{r}