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Note: The empty set symbol ∅ looks similar, but is unrelated to the Greek letter. or represents: the golden ratio 1.618... in mathematics, art, and architecture; Euler's totient function in number theory; the argument of a complex number in mathematics; the value of a plane angle in physics and mathematics
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
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.
This list is incomplete; you can help by adding missing items. ( January 2011 ) 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.
Minakshisundaram–Pleijel zeta function of a Laplacian; Motivic zeta function of a motive; Multiple zeta function, or Mordell–Tornheim zeta function of several variables; p-adic zeta function of a p-adic number; Prime zeta function, like the Riemann zeta function, but only summed over primes; Riemann zeta function, the archetypal example ...
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.
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; Modern Greek: zíta) is the sixth letter of the Greek alphabet.
Smoothness is a concept which mathematics has endowed with many meanings, from simple differentiability to infinite differentiability to analyticity, and still others which are more complicated. Each such usage attempts to invoke the physically intuitive notion of smoothness. strong, stronger