Xi (letter)
Look up Ξ or ξ in Wiktionary, the free dictionary. 
Greek alphabet  



History  
Use in other languages  
Related topics  
 
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.^{[1]} 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.
Greek
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.
Cyrillic
While having no Latin derivative, the Xi was adopted into the early Cyrillic alphabet, as the letter ksi (Ѯ, ѯ).
Mathematics and science
Upper case
The uppercase 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
 HarishChandra's Ξ function
 The Riemann Xi function
 Ether currency of Ethereum
Lower case
The lowercase 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^{[2]} 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 HbPortland (ξ_{2}γ_{2}) and HbGower I (ξ_{2}ε_{2})
 The correlation function in astronomy
 Spatial frequency;^{[3]} 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 xcoordinate of computational space as used in computational fluid dynamics
 Potential difference in physics (in volts)
 The radial integral in the spinorbit 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
Character encodings
 Greek Xi / Coptic Ksi
Character  Ξ  ξ  Ⲝ  ⲝ  

Unicode name  GREEK CAPITAL LETTER XI  GREEK SMALL LETTER XI  COPTIC CAPITAL LETTER KSI  COPTIC SMALL LETTER KSI  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  926  U+039E  958  U+03BE  11420  U+2C9C  11421  U+2C9D 
UTF8  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 Greek2  189  BD  232  E8  
Windows 1253  206  CE  238  EE  
TeX  \Xi  \xi 
^{[4]}
 Mathematical Xi
Character  𝚵  𝛏  𝛯  𝜉  𝜩  𝝃  

Unicode name  MATHEMATICAL BOLD CAPITAL XI  MATHEMATICAL BOLD SMALL XI  MATHEMATICAL ITALIC CAPITAL XI  MATHEMATICAL ITALIC SMALL XI  MATHEMATICAL BOLD ITALIC CAPITAL XI  MATHEMATICAL BOLD ITALIC SMALL XI  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120501  U+1D6B5  120527  U+1D6CF  120559  U+1D6EF  120585  U+1D709  120617  U+1D729  120643  U+1D743 
UTF8  240 157 154 181  F0 9D 9A B5  240 157 155 143  F0 9D 9B 8F  240 157 155 175  F0 9D 9B AF  240 157 156 137  F0 9D 9C 89  240 157 156 169  F0 9D 9C A9  240 157 157 131  F0 9D 9D 83 
UTF16  55349 57013  D835 DEB5  55349 57039  D835 DECF  55349 57071  D835 DEEF  55349 57097  D835 DF09  55349 57129  D835 DF29  55349 57155  D835 DF43 
Numeric character reference  𝚵  𝚵  𝛏  𝛏  𝛯  𝛯  𝜉  𝜉  𝜩  𝜩  𝝃  𝝃 
Character  𝝣  𝝽  𝞝  𝞷  

Unicode name  MATHEMATICAL SANSSERIF BOLD CAPITAL XI  MATHEMATICAL SANSSERIF BOLD SMALL XI  MATHEMATICAL SANSSERIF BOLD ITALIC CAPITAL XI  MATHEMATICAL SANSSERIF BOLD ITALIC SMALL XI  
Encodings  decimal  hex  decimal  hex  decimal  hex  decimal  hex 
Unicode  120675  U+1D763  120701  U+1D77D  120733  U+1D79D  120759  U+1D7B7 
UTF8  240 157 157 163  F0 9D 9D A3  240 157 157 189  F0 9D 9D BD  240 157 158 157  F0 9D 9E 9D  240 157 158 183  F0 9D 9E B7 
UTF16  55349 57187  D835 DF63  55349 57213  D835 DF7D  55349 57245  D835 DF9D  55349 57271  D835 DFB7 
Numeric character reference  𝝣  𝝣  𝝽  𝝽  𝞝  𝞝  𝞷  𝞷 
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.
Other uses
Upper case Ξ is used as an 'E' to stylize company names/logos like Razer (styled as RΛZΞR) and musician Banners (styled as BANNΞRS)
References
 ↑ "xi". New Oxford American Dictionary, 2nd Edition.
 ↑ IUPAC Gold Book Entry: "Extent of Reaction" Archived June 29, 2012, at the Wayback Machine.
 ↑ SPIE Optipedia article: "Spatial Frequency"
 ↑ Unicode Code Charts: Greek and Coptic (Range: 037003FF)