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# 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 1018 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 (ξ2γ2) and Hb-Gower I (ξ2ε2)

• 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:

 Greek Alphabet Symbol Letter Symbol Letter Uppercase Lowercase Uppercase Lowercase Α α Alpha Ν ν Nu Β β Beta Ξ ξ Xi Γ γ Gamma Ο ο Omicron Δ δ Delta Π π Pi Ε ε Epsilon Ρ ρ Rho Ζ ζ Zeta Σ σ Sigma Η η Eta Τ τ Tau Θ θ Theta Υ υ Upsilon Ι ι Iota Φ φ Phi Κ κ Kappa Χ χ Chi Λ λ Lambda Ψ ψ Psi Μ μ Mu Ω ω Omega

### Sources

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

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