TeXipedia

varPi

Represents an uppercase pi variant commonly used in mathematical expressions where a distinct form of pi is needed.

Overview

Serves as an alternative representation of the uppercase Pi symbol, particularly useful in mathematical contexts where multiple pi-like symbols are needed to represent different concepts or variables.

  • Often employed in advanced mathematics and theoretical physics.
  • Helpful for distinguishing between different mathematical objects or operators involving pi.
  • Frequently appears in set theory, category theory, and mathematical analysis where multiple pi symbols are required.
  • Provides visual distinction from the standard \Pi symbol while maintaining semantic connection to pi-related concepts.

Examples

Using the variant Pi symbol in a product formula for infinite series.

Πn=1(1+1n2)\varPi_{n=1}^{\infty} \left(1 + \frac{1}{n^2}\right)
\varPi_{n=1}^{\infty} \left(1 + \frac{1}{n^2}\right)

Representing a permutation group with variant Pi notation.

Π={(1,2,3),(2,3,1),(3,1,2)}\varPi = \{(1,2,3), (2,3,1), (3,1,2)\}
\varPi = \{(1,2,3), (2,3,1), (3,1,2)\}

Using variant Pi in statistical probability notation.

P(AB)=P(BA)P(A)Π(B)P(A \mid B) = \frac{P(B \mid A)P(A)}{\varPi(B)}
P(A \mid B) = \frac{P(B \mid A)P(A)}{\varPi(B)}