Analytic expression (nonfiction): Difference between revisions
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In [[Mathematics (nonfiction)|mathematics]], an '''analytic expression''' (or '''expression in analytic form''') is a [[ | In [[Mathematics (nonfiction)|mathematics]], an '''analytic expression''' (or '''expression in analytic form''') is a [[Expression (nonfiction)|mathematical expression]] constructed using well-known operations that lend themselves readily to calculation. | ||
== Discussion == | == Discussion == | ||
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== Nonfiction cross-reference == | == Nonfiction cross-reference == | ||
* [[Closed-form expression (nonfiction)]] - a [[ | * [[Closed-form expression (nonfiction)]] - a [[Expression (nonfiction)|mathematical expression]] expressed using a finite number of standard operations. It may contain constants, variables, certain "well-known" operations (e.g., + − × ÷), and functions (e.g., nth root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit, differentiation or integration. The set of operations and functions admitted in a closed-form expression may vary with author and context. | ||
* [[Mathematics (nonfiction)]] | * [[Mathematics (nonfiction)]] | ||
Latest revision as of 06:58, 24 April 2020
In mathematics, an analytic expression (or expression in analytic form) is a mathematical expression constructed using well-known operations that lend themselves readily to calculation.
Discussion
Similar to closed-form expressions, the set of well-known functions allowed can vary according to context but always includes the basic arithmetic operations (addition, subtraction, multiplication, and division), exponentiation to a real exponent (which includes extraction of the nth root), logarithms, and trigonometric functions.
However, the class of expressions considered to be analytic expressions tends to be wider than that for closed-form expressions. In particular, special functions such as the Bessel functions and the gamma function are usually allowed, and often so are infinite series and continued fractions. On the other hand, limits in general, and integrals in particular, are typically excluded.[citation needed]
If an analytic expression involves only the algebraic operations (addition, subtraction, multiplication, division, and exponentiation to a rational exponent) and rational constants then it is more specifically referred to as an algebraic expression.
In the News
Fiction cross-reference
Nonfiction cross-reference
- Closed-form expression (nonfiction) - a mathematical expression expressed using a finite number of standard operations. It may contain constants, variables, certain "well-known" operations (e.g., + − × ÷), and functions (e.g., nth root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit, differentiation or integration. The set of operations and functions admitted in a closed-form expression may vary with author and context.
- Mathematics (nonfiction)
External links
- Closed-form expression @ Wikipedia