Xi (letter)

The uppercase letter Ξ is used as a symbol in various contexts.

• Harish-Chandra's Ξ function in harmonic analysis and representation theory
• The Riemann Xi function in analytic number theory and complex analysis

• The "cascade particles" in particle physics
• The partition function under the grand canonical ensemble in statistical mechanics

• 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

The lowercase letter ξ is used as a symbol for:

• 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

• In fluid dynamics, the Iribarren parameter.
• The initial mass function in astronomy.
• The correlation function in astronomy.
• Spatial frequency;[2] 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

• Propositional variables in some philosophical works, first found in Wittgenstein's Tractatus
• Extent of reaction, a concept in physical chemistry[3] used often in chemical engineering kinetics and thermochemistry
• Unknown stereochemistry or stereocentre configuration in a planar ring system in organic chemistry,[4] as well as uppercase Xi for unknown R/S/E/Z configuration in general[5]
• 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.

Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)

The following 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.