# Xi (Ξ, ξ) Definition

Xi (Ξ, ξ) is the 14th letter of the Greek Alphabet. In the system of Greek Numerals, it has a value of 60. Xi was derived from the Phoenician letter samekh. Xi is distinct from the letter chi, which gave its form to the Latin letter X.

## Usage in Mathematics & Science

The uppercase Xi (Ξ) is used for:

The cascade particles in particle physics

Indicating no change of state in Z notation

The partition function under the grand canonical ensemble in statistical mechanics

Harish-Chandra's Ξ function

The Riemann Xi function

Monetary units of the cryptocurrency Ether, equal to 10

^{18}Wei

The lowercase Xi (ξ) is used for:

Random variables

Propositional variables in some philosophical works, first found in Wittgenstein's Tractatus

Dimensionless distance variable used in the Lane–Emden equation

Extent of reaction, a concept in physical chemistry used often in chemical engineering kinetics and thermochemistry

Unknown stereochemistry or stereocentre configuration in a planar ring system in organic chemistry, as well as uppercase Xi for unknown R/S/E/Z configuration in general

Eigenvectors

Damping Ratio C/Ccr(vibrational analysis)

A parameter in a generalized Pareto distribution

The symmetric function equation of the Riemann zeta function in mathematics, also known as the Riemann Xi function

A universal set in set theory

A number used in the remainder term of Taylor's theorem that falls between the limits a and b

A number used in error approximations for formulas that are applications of Taylor's theorem, such as Newton–Cotes formulas

One of the two different polypeptide chains of the human embryonic hemoglobin types Hb-Portland (ξ

_{2}γ_{2}) and Hb-Gower I (ξ_{2}ε_{2})The initial mass function in astronomy.

The correlation function in astronomy.

Spatial frequency, also sometimes temporal frequency.

A small displacement in MHD plasma stability theory

A parameter denoted as warped time used to derive the equations for homogeneous azeotropic distillation

The x-coordinate of computational space as used in computational fluid dynamics

Potential difference in physics (in volts)

The radial integral in the spin-orbit matrix operator in atomic physics.

The Killing vector in general relativity.

Average logarithmic energy decrement per collision (neutron calculations in nuclear physics)

Pippard's cohesion length in superconductors

State Price Density in mathematical finance

The diameter of a crystal nucleus in nucleation theory

Microturbulence velocity in a stellar atmosphere

The information vector in the Information Filter, GraphSLAM, and a number of other algorithms used for robot localization and robotic mapping.

The dimensionless longitudinal momentum loss of a beam particle after a two-body interaction in accelerator physics.

## Greek Alphabet

The letters of the Ancient Greek Alphabet, which are frequently utilized in math and science:

### Related Definitions

### Sources

“Xi (Letter).” Wikipedia, Wikimedia Foundation, 6 Apr. 2020, en.wikipedia.org/wiki/Xi_(letter).