Xi (letter)

Xi is the fourteenth letter of the Greek alphabet (uppercase Ξ, lowercase ξ; ξι), representing the voiceless consonant cluster ks. Its name is pronounced ksi in Modern Greek, and generally zaɪ or ksaɪ in English. 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. 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 Sicily 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. The Xi was adopted into the early Cyrillic alphabet, as the letter ksi (Ѯ, ѯ). 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 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.