Xi

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Ξξ Xi
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'''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 language|English]].<sup>[1]</sup> In the system of [[Greek numerals]], it has a value of 60.
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Xi is not to be confused with the letter [[chi (letter)|chi]], which gave its form to the Latin letter [[X]].
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==Greek==
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[[Image:Xi alternate.png|thumb|left|A joined variant of Ξ.]]
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Both in [[Modern Greek]] and in the modern system for writing [[Ancient Greek]], xi represents /ks/. This usage comes from the [[History of the Greek alphabet#Epichoric alphabets|regional variants]] of the Greek alphabet used to write the [[Attic Greek|Attic]] and [[Ionic Greek|Ionic]] [[Ancient Greek dialects|dialects]].
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In the Western or [[Euboean alphabet]], the sounds represented by xi and [[chi (letter)|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]].
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==Cyrillic==
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While having no Latin derivative, the Xi was adopted into the [[early Cyrillic alphabet]], as the letter [[Ksi (Cyrillic letter)|ksi]] (Ѯ, ѯ).
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==Math and science==
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===Upper case===
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The upper-case letter Ξ is used as symbol for:
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* The "[[Xi (particle)|cascade particles]]" in particle physics
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* Indicating "no change of state" in [[Z notation]]
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* The [[Partition function (statistical mechanics)|partition function]] under the [[grand canonical ensemble]] in statistical mechanics
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===Lower case===
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The lower-case letter ξ is used as a symbol for:
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* [[Random variable]]s
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* Dimensionless distance variable used in the [[Lane-Emden equation]]
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* [[Extent of reaction]] (a topic found most often in [[chemical engineering]] kinetics)
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* [[Eigenvector]]s
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* Damping Ratio C/Ccr(vibrational analysis)
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* A parameter in a [[Pareto distribution#Generalized Pareto distribution|generalized Pareto distribution]]
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* The symmetric function equation of the [[Riemann zeta function]] in [[mathematics]], also known as the [[Riemann Xi function]]
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* A universal set in the [[set theory]]
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* A number used in the error term of [[Newton–Cotes formulas]] that falls between ''a'' and ''b''
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* One of the two different polypeptide chains of the human embryonic [[hemoglobin]] types Hb-Portland (ξ<sub>2</sub>γ<sub>2</sub>) and Hb-Gower I (ξ<sub>2</sub>ε<sub>2</sub>)
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* The [[correlation function (astronomy)|correlation function]] in [[astronomy]]
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* Frequency
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* A small displacement in MHD [[plasma stability]] theory
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* A parameter denoted as [[warped time]] used to derive the equations for homogeneous azeotropic distillation
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* The x-coordinate of computational space as used in [[Computational Fluid Dynamics]]
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* Potential difference in physics (in volts)
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* The radial integral in the spin-orbit matrix operator in [[atomic physics]].
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* The [[Killing vector]] in General Relativity.
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* Average Logarithmic Energy Decrement per Collision (neutron calculations in nuclear physics)
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== References ==
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{{DEFAULTSORT:Xi (Letter)}}
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[[Category:Greek letters]]

Revision as of 12:29, 18 March 2011

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.

Contents

Greek

A joined variant of Ξ.
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:

Lower case

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

References

Retrieved from "http://textus-receptus.com/wiki/Xi"
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