# Xi (letter)

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**Xi** (uppercase **Ξ**, lowercase **ξ**; Greek: ξι) is the 14th letter of the Greek alphabet. It is pronounced [ksi] in Modern Greek, and generally /zaɪ/ or /saɪ/ in English.^{[1]} In the system of Greek numerals, it has a value of 60. Xi was derived from the Phoenician letter samekh .

Xi is distinct from 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).

## Mathematics and science

### Uppercase

The uppercase 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
- Monetary units of the cryptocurrency Ether, equal to 10
^{18}Wei

### Lowercase

The lowercase letter ξ is used as a symbol for:

- Random variables
- Propositional variables in some philosophical works, first found in Wittgenstein's Tractatus
- Dimensionless distance variable used in the Lane–Emden equation
- Extent of reaction, a concept in physical chemistry
^{[2]}used often in chemical engineering kinetics and thermochemistry - Unknown stereochemistry or stereocentre configuration in a planar ring system in organic chemistry
^{[3]}, as well as uppercase Xi for unknown*R*/*S*/*E*/*Z*configuration in general^{[4]} - 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 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 (ξ
_{2}γ_{2}) and Hb-Gower I (ξ_{2}ε_{2}) - The initial mass function in astronomy.
- The correlation function in astronomy.
- Spatial frequency;
^{[5]}also sometimes temporal 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)
- Pippard's cohesion length in superconductors
- State Price Density in mathematical finance
- The diameter of a crystal nucleus in nucleation theory
- Microturbulence velocity in a stellar atmosphere
- The information vector in the Information Filter, GraphSLAM, and a number of other algorithms used for robot localization and robotic mapping.
- The dimensionless longitudinal momentum loss of a beam particle after a two-body interaction in accelerator physics.

## Character encodings

- Greek Xi / Coptic Ksi

Character | Ξ | ξ | Ⲝ | ⲝ | ||||
---|---|---|---|---|---|---|---|---|

Unicode name |
GREEK CAPITAL LETTER XI | GREEK LOWERCASE LETTER XI | COPTIC CAPITAL LETTER KSI | COPTIC LOWERCASE LETTER KSI | ||||

Encodings | decimal | hex | decimal | hex | decimal | hex | decimal | hex |

Unicode | 926 | U+039E | 958 | U+03BE | 11420 | U+2C9C | 11421 | U+2C9D |

UTF-8 | 206 158 | CE 9E | 206 190 | CE BE | 226 178 156 | E2 B2 9C | 226 178 157 | E2 B2 9D |

Numeric character reference | Ξ | Ξ | ξ | ξ | Ⲝ | Ⲝ | ⲝ | ⲝ |

Named character reference | Ξ | ξ | ||||||

DOS Greek | 141 | 8D | 165 | A5 | ||||

DOS Greek-2 | 189 | BD | 232 | E8 | ||||

Windows 1253 | 206 | CE | 238 | EE | ||||

TeX | \Xi | \xi |

^{[6]}

- Mathematical Xi

Character | 𝚵 | 𝛏 | 𝛯 | 𝜉 | 𝜩 | 𝝃 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Unicode name |
MATHEMATICAL BOLD CAPITAL XI |
MATHEMATICAL BOLD LOWERCASE XI |
MATHEMATICAL ITALIC CAPITAL XI |
MATHEMATICAL ITALIC LOWERCASE XI |
MATHEMATICAL BOLD ITALIC CAPITAL XI |
MATHEMATICAL BOLD ITALIC LOWERCASE XI | ||||||

Encodings | decimal | hex | decimal | hex | decimal | hex | decimal | hex | decimal | hex | decimal | hex |

Unicode | 120501 | U+1D6B5 | 120527 | U+1D6CF | 120559 | U+1D6EF | 120585 | U+1D709 | 120617 | U+1D729 | 120643 | U+1D743 |

UTF-8 | 240 157 154 181 | F0 9D 9A B5 | 240 157 155 143 | F0 9D 9B 8F | 240 157 155 175 | F0 9D 9B AF | 240 157 156 137 | F0 9D 9C 89 | 240 157 156 169 | F0 9D 9C A9 | 240 157 157 131 | F0 9D 9D 83 |

UTF-16 | 55349 57013 | D835 DEB5 | 55349 57039 | D835 DECF | 55349 57071 | D835 DEEF | 55349 57097 | D835 DF09 | 55349 57129 | D835 DF29 | 55349 57155 | D835 DF43 |

Numeric character reference | 𝚵 | 𝚵 | 𝛏 | 𝛏 | 𝛯 | 𝛯 | 𝜉 | 𝜉 | 𝜩 | 𝜩 | 𝝃 | 𝝃 |

Character | 𝝣 | 𝝽 | 𝞝 | 𝞷 | ||||
---|---|---|---|---|---|---|---|---|

Unicode name |
MATHEMATICAL SANS-SERIF BOLD CAPITAL XI |
MATHEMATICAL SANS-SERIF BOLD LOWERCASE XI |
MATHEMATICAL SANS-SERIF BOLD ITALIC CAPITAL XI |
MATHEMATICAL SANS-SERIF BOLD ITALIC LOWERCASE XI | ||||

Encodings | decimal | hex | decimal | hex | decimal | hex | decimal | hex |

Unicode | 120675 | U+1D763 | 120701 | U+1D77D | 120733 | U+1D79D | 120759 | U+1D7B7 |

UTF-8 | 240 157 157 163 | F0 9D 9D A3 | 240 157 157 189 | F0 9D 9D BD | 240 157 158 157 | F0 9D 9E 9D | 240 157 158 183 | F0 9D 9E B7 |

UTF-16 | 55349 57187 | D835 DF63 | 55349 57213 | D835 DF7D | 55349 57245 | D835 DF9D | 55349 57271 | D835 DFB7 |

Numeric character reference | 𝝣 | 𝝣 | 𝝽 | 𝝽 | 𝞝 | 𝞝 | 𝞷 | 𝞷 |

These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

## Other uses

*Media related to Letter "E" as "Ξ" at Wikimedia Commons*

Uppercase Ξ is used as an 'E' to stylise company names/logos like Razer (styled as **RΛZΞR**) and musicman Banners (styled as **BANNΞRS**). (Compare: Heavy Metal umlaut; Faux Cyrillic)

## References

Look up or Ξ in Wiktionary, the free dictionary.ξ |

**^**"xi". New Oxford American Dictionary, 2nd Edition.**^**IUPAC Gold Book Entry: "Extent of Reaction" Archived June 29, 2012, at the Wayback Machine**^**John Buckingham; Caroline M. Cooper; Rupert Purchase (18 November 2015).*Natural Products Desk Reference*. CRC Press. pp. 53–. ISBN 978-1-4398-7362-5.**^***Nomenclature of Organic Chemistry: IUPAC Recommendations and Preferred Names*. p. 1159–1160. Retrieved 11 September 2017.**^**SPIE Optipedia article: "Spatial Frequency"**^**Unicode Code Charts: Greek and Coptic (Range: 0370-03FF)