Xi

From Wikipedia, the free encyclopedia

Greek alphabet
Αα Alpha	Νν Nu
Ββ Beta	Ξξ Xi
Γγ Gamma	Οο Omicron
Δδ Delta	Ππ Pi
Εε Epsilon	Ρρ Rho
Ζζ Zeta	Σσς Sigma
Ηη Eta	Ττ Tau
Θθ Theta	Υυ Upsilon
Ιι Iota	Φφ Phi
Κκ Kappa	Χχ Chi
Λλ Lambda	Ψψ Psi
Μμ Mu	Ωω Omega
Obsolete letters
Digamma	Qoppa
San	Sampi
Greek diacritics

Xi (uppercase Ξ, lowercase ξ) is the 14th letter of the Greek alphabet. It is pronounced [ksi] in Modern Greek, and generally pronounced /ˈsaɪ/ (UK) or /ˈzaɪ/ (US) in English. In the system of Greek numerals, it has a value of 60. The Xi is not to be confused with the letter Chi, which takes the form of the Latin letter X. In ancient times, the Western Greek alphabet used it to represent /kʰ/, while it was used to represent /ks/ in other alphabets. As the alphabet was standardized, Xi was decided to be used for /ks/ and Chi for /kʰ/. While having no Latin derivative, the Xi was adopted into the early Cyrillic alphabet, as the letter ksi (Ѯ, ѯ).

The lower-case letter ξ is used as a symbol for

• random variables;
• extent of reaction (a topic found most often in chemical engineering kinetics);
• eigenvectors;
• 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;
• the damping factor in an RLC circuit;
• a universal set in the set theory;
• a number used in the error term of Newton–Cotes formulas that falls between a and b;
• one of the two different polypeptide chains of the human embryonic hemoglobin types Hb-Portland (ξ₂γ₂) and Hb-Gower I (ξ₂ε₂);
• the correlation function in astronomy;
• frequency;
• a small displacement in MHD plasma stability theory.

The upper-case letter Ξ is used as symbol for

• The 'cascade particles' in particle physics;
• indicating "no change of state" in Z notation.