Xi

Xi (uppercase Ξ, lowercase ξ) is the 14th letter of the Greek alphabet. It is pronounced|ksi in Modern Greek, and generally pronEng|ˈsaɪ (UK) or IPA|/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 gave its form to the Latin letter X. In ancient times, the Western Greek alphabet used it to represent IPA|/kʰ/, while it was used to represent IPA|/ks/ in other alphabets. As the alphabet was standardized, Xi was decided to be used for IPA|/ks/ and Chi for IPA|/kʰ/. While having no Latin derivative, the Xi was adopted into the early Cyrillic alphabet, as the letter ksi (Unicode|Ѯ, Unicode|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;
*income elasticity in the field of Economics.

The upper-case letter Ξ is used as symbol for
*The 'cascade particles' in particle physics;
*indicating "no change of state" in Z notation.