Uppercase The uppercase letter Ξ is used as a symbol in various contexts.
Pure mathematics •
Harish-Chandra's Ξ function in
harmonic analysis and
representation theory • The
Riemann Xi function in
analytic number theory and
complex analysis Physics • The "
cascade particles" in particle physics • The
partition function under the
grand canonical ensemble in statistical mechanics
Other uses • Indicating "no change of state" in
Z notation in
computing • Used as the
Latin letter
E in some logos. • Monetary units of the
cryptocurrencies Ether (and less commonly
ETC), equal to 1018 Wei
Lowercase The lowercase letter ξ is used as a symbol for:
Pure mathematics •
Random variables • 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 Physics and astronomy • In fluid dynamics, the
Iribarren parameter. • 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 • 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 • The diameter of a crystal nucleus in
nucleation theory •
Microturbulence velocity in a stellar atmosphere • The dimensionless longitudinal momentum loss of a beam particle after a two-body interaction in accelerator physics. • Dimensionless distance variable used in the
Lane–Emden equation Other uses • Propositional variables in some philosophical works, first found in Wittgenstein's
Tractatus •
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 • One of the two different polypeptide chains of the human embryonic
hemoglobin types Hb-Portland (ξ2γ2) and Hb-Gower I (ξ2ε2) • A parameter denoted as
warped time used to derive the equations for homogeneous
azeotropic distillation • State Price Density in
mathematical finance • The information vector in the
Information Filter,
GraphSLAM, and a number of other algorithms used for
robot localization and
robotic mapping. • Used in
Support Vector machines in cases where the data is not
linearly separable. • Used in
Microelectronics to represent the distance from a
p-n junction to a point in the
depletion region where the
electric field is strongest. ==Other uses==