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Closed-form expressions are an important sub-class of analytic expressions, which contain a finite number of applications of well-known functions. Unlike the broader analytic expressions, the closed-form expressions do not include infinite series or continued fractions ; neither includes integrals or limits .
The Dottie number appears in the closed form expression of some integrals: [6] [7] ... Another closed form representation: = ...
The number in the n-th month is the n-th Fibonacci number. [20] The name "Fibonacci sequence" was first used by the 19th-century number theorist Édouard Lucas. [21] Solution to Fibonacci rabbit problem: In a growing idealized population, the number of rabbit
The following is a useful property to calculate low-integer-order polylogarithms recursively in closed form: ... even when the series contains a large number of ...
Explicit formula can refer to: . Closed-form expression, a mathematical expression in terms of a finite number of well-known functions; Analytical expression, a mathematical expression in terms of a finite or infinite number of well-known functions
An elementary number is one formalization of the concept of a closed-form number. The elementary numbers form an algebraically closed field containing the roots of arbitrary expressions using field operations, exponentiation, and logarithms. The set of the elementary numbers is subdivided into the explicit elementary numbers and the implicit ...
In mathematics, a subset of a given set is closed under an operation of the larger set if performing that operation on members of the subset always produces a member of that subset. For example, the natural numbers are closed under addition, but not under subtraction: 1 − 2 is not a natural number, although both 1 and 2 are.
In mathematics, the Jacobsthal numbers are an integer sequence named after the German mathematician Ernst Jacobsthal.Like the related Fibonacci numbers, they are a specific type of Lucas sequence (,) for which P = 1, and Q = −2 [1] —and are defined by a similar recurrence relation: in simple terms, the sequence starts with 0 and 1, then each following number is found by adding the number ...