Xi (uppercase Ξ, lowercase ξ; Greek: ξι) is the 14th letter of the Greek alphabet. It is pronounced [ksi] in Modern Greek, and generally /ˈzaɪ/ or /ˈsaɪ/ in English. In the system of Greek numerals, it has a value of 60. Xi was derived from the Phoenician letter samekh .
Xi is not to be confused with the letter chi, which gave its form to the Latin letter X.
Both in classical Ancient Greek and in Modern Greek, the letter Ξ represents the sound [ks]. In some archaic local variants of the Greek alphabet, this letter was missing. Instead, especially in the dialects of most of the Greek mainland and Euboea, the sound [ks] was represented by Χ (which in classical Greek is chi, used for /kʰ/). Because this variant of the Greek alphabet was used in Italy, the Latin alphabet borrowed Χ rather than Ξ as the Latin letter X.
While having no Latin derivative, the Xi was adopted into the early Cyrillic alphabet, as the letter ksi (Ѯ, ѯ).
The upper-case letter Ξ is used as symbol 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
Ether currency of Ethereum
The lower-case letter ξ is used as a symbol 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
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 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
Greek Xi / Coptic Ksi
Mathematical Xi
These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.
Upper case Ξ is used as an 'E' to stylize company names/logos like Razer (styled as RΛZΞR) and musician Banners (styled as BANNΞRS)
