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The omega constant is a mathematical constant defined as the unique real number that satisfies the equation = It is the value of W(1), where W is Lambert's W function. The name is derived from the alternate name for Lambert's W function, the omega function. The numerical value of Ω is given by
The notation convention chosen here (with W 0 and W −1) follows the canonical reference on the Lambert W function by Corless, Gonnet, Hare, Jeffrey and Knuth. [3]The name "product logarithm" can be understood as follows: since the inverse function of f(w) = e w is termed the logarithm, it makes sense to call the inverse "function" of the product we w the "product logarithm".
For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set.
The circumference of a circle with diameter 1 is π.. A mathematical constant is a number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
A new collection of short problems and the answers to some of "life's" 1970 Dec: The paradox of the nontransitive dice and the elusive principle of indifference 1971 Jan: Lessons from Dr. Matrix in chess and numerology 1971 Feb: On cellular automata, self-reproduction, the Garden of Eden and the game "life" 1971 Mar
One of the main applications of this function is in the resolution of the equation z = ln(z), as the only solution is given by z = e −ω(π i).. y = ω(z) is the unique solution, when for x ≤ −1, of the equation y + ln(y) = z.
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The prime omega function (), giving the number of distinct prime factors of Topics referred to by the same term This disambiguation page lists mathematics articles associated with the same title.