Xi (letter)
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Xi is the name of the 14th letter of the Greek alphabet (uppercase Ξ or Ξ, lowercase ξ; Greek: ξι). It is pronounced [ksi] in Modern Greek, and generally /zaɪ/ or /ksaɪ/ in English.[1] 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.
Greek[]
Both in classical Ancient Greek and in Modern Greek, the letter Ξ represents the consonant cluster /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 cluster /ks/ was represented by Χ (which in classical Greek is chi, used for /kʰ/).
Because this variant of the Greek alphabet was used in Magna Graecia (the Greek colonies in Sicilly and the southern part of the Italian peninsula), the Latin alphabet borrowed Χ rather than Ξ as the Latin letter that represented the /ks/ cluster that was also present in Latin.
Cyrillic[]
The Xi was adopted into the early Cyrillic alphabet, as the letter ksi (Ѯ, ѯ).
Mathematics and science[]
Uppercase[]
The uppercase letter Ξ is used as 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
- 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;[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)
- 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[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]
- Damping Ratio C/Ccr(vibrational analysis)
- 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 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.
Character encodings[]
Greek Xi / Coptic Ksi[]
Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)
Preview | Ξ | ξ | Ⲝ | ⲝ | ||||
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Unicode name | GREEK CAPITAL LETTER XI | GREEK LOWERCASE LETTER XI | COPTIC CAPITAL LETTER KSI | COPTIC LOWERCASE LETTER KSI | ||||
Encodings | decimal | hex | dec | hex | dec | hex | dec | hex |
Unicode | 926 | U+039E | 958 | U+03BE | 11420 | U+2C9C | 11421 | U+2C9D |
UTF-8 | 206 158 | CE 9E | 206 190 | CE BE | 226 178 156 | E2 B2 9C | 226 178 157 | E2 B2 9D |
Numeric character reference | Ξ |
Ξ |
ξ |
ξ |
Ⲝ |
Ⲝ |
ⲝ |
ⲝ |
Named character reference | Ξ | ξ | ||||||
DOS Greek | 141 | 8D | 165 | A5 | ||||
DOS Greek-2 | 189 | BD | 232 | E8 | ||||
Windows 1253 | 206 | CE | 238 | EE | ||||
TeX | \Xi | \xi |
Mathematical Xi[]
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.
Preview |
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