Xi

From Textus Receptus

Xi

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

A joined variant of Ξ.

Both in Modern Greek and in the modern system for writing Ancient Greek, xi represents /ks/. This usage comes from the regional variants of the Greek alphabet used to write the Attic and Ionic dialects.

In the Western or Euboean alphabet, the sounds represented by xi and chi were the opposite of the modern usage: xi represented /kʰ/, and chi (Χ) represented /ks/. Because this variant of the Greek alphabet was used in Italy, the Latin alphabet borrowed chi rather than xi 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

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 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

Majuscule form
Α	Β	Γ	Δ	Ε	Ζ	Η	Θ	Ι	Κ	Λ	Μ	Ν	Ξ	Ο	Π	Ρ	Σ	Τ	Υ	Φ	Χ	Ψ	Ω
Minuscule form
α	β	γ	δ	ε	ζ	η	θ	ι	κ	λ	μ	ν	ξ	ο	π	ρ	σ	τ	υ	φ	χ	ψ	ω

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