Xi (letter)

Xi (uppercase Ξ, lowercase ξ) is the 14th letter of the Greek alphabet. It is pronounced [ˈksi] in Modern Greek, and generally /ˈzaɪ/ or /ˈsaɪ/ in English.^[1] In the system of Greek numerals, it has a value of 60.

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).

Math and science

Upper case

The upper-case 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
• Harish-Chandra's Ξ function
• The Riemann Xi function

Lower case

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

• Random variables
• Dimensionless distance variable used in the Lane–Emden equation
• Extent of reaction (a topic found most often in chemical engineering kinetics)
• 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 the 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 Hb-Portland (ξ₂γ₂) and Hb-Gower I (ξ₂ε₂)
• The correlation function in astronomy
• 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 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)

References

1. ^ "xi". New Oxford American Dictionary, 2nd Edition.