Xi (letter)

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
Other characters
	Digamma		Stigma
	Heta		San
	Qoppa		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 /ˈzaɪ/ or /ˈksaɪ/ in English.^[1] 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 /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).

It should not be confused with ≡ (equivalence sign, Unicode hex 2261).

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

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

A joined variant of Ξ.

• 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 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
• 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.