Pi

Pi, the 16^th Greek letter, written in lowercase as π and capitalized as Π (sometimes written $\mathrm {][}$), can refer to the following mathematical concepts.

• pi (constant) - $\pi \approx 3.14159\ldots$, representing the ratio of a circle's circumference to its diameter (also known as Archimedes' number)
• Product operator Π — e.g., $\prod _{i=0}^{n}f(i)$. (See also product of a sequence.) It is functionally similar to summation notation, using $\sum _{i=0}^{n}$, which is the sum of a sequence.
• Prime counting function π(x). (See also prime numbers.) A function defined to return a value equal to the quantity of prime numbers less than or equal to its inputted value.
• The transformation (horizontal shift) of the Gamma function: $\Pi(x)=\Gamma(x+1)$.
  • The reciprocal of its capitalized counterpart: $\pi (x)={\frac {1}{\Pi (x)}}$.
• The upside down capital represent Coproducts: $\coprod _{j\in J}$