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Sometimes, font variants of Greek letters are used as distinct symbols in mathematics, in particular for ε/ϵ and π/ϖ. The archaic letter digamma (Ϝ/ϝ/ϛ) is sometimes used. The Bayer designation naming scheme for stars typically uses the first Greek letter, α, for the brightest star in each constellation, and runs through the alphabet ...
The Riemann zeta function ζ(z) plotted with domain coloring. [1] The pole at = and two zeros on the critical line.. The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (), is a mathematical function of a complex variable defined as () = = = + + + for >, and its analytic continuation elsewhere.
Zeta (UK: / ˈ z iː t ə /, US: / ˈ z eɪ t ə /; [1] uppercase Ζ, lowercase ζ; Ancient Greek: ζῆτα, Demotic Greek: ζήτα, classical [d͡zɛ̌ːta] or zē̂ta; Greek pronunciation: zíta) is the sixth letter of the Greek alphabet.
The following 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: U+1D6B5 횵 MATHEMATICAL BOLD CAPITAL XI; U+1D6CF 훏 MATHEMATICAL BOLD SMALL XI; U+1D6EF 훯 MATHEMATICAL ITALIC CAPITAL XI; U+1D709 휉 MATHEMATICAL ITALIC ...
Latin and Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities.
Zeta with caron: Nonstandard letter for Cypriot Greek [9] and Pontic Greek [10] representing /ʒ/ Ζ̇ ζ̇: Zeta with dot above: Arvanitika letter for /ʒ/ [7] Ήή: Eta with acute: High pitch on short vowel or rising pitch on long vowel Ὴὴ: Eta with grave: Archaic letter indicating normal or low pitch ῆ: Eta with circumflex
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The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.