Analytical expression
Encyclopedia
In mathematics
, an analytical expression (or expression in analytical form) is a mathematical expression, constructed using well-known operations that lend themselves readily to calculation. As for closed-form expression
s, the criteria are not precisely defined, but the class of expressions considered to be "analytical expressions" tends to be wider.
In particular, special functions
such as the Bessel functions and the gamma function
are usually allowed, and often so are infinite series and continued fraction
s. On the other hand, limits
in general, and integral
s in particular, are typically excluded.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, an analytical expression (or expression in analytical form) is a mathematical expression, constructed using well-known operations that lend themselves readily to calculation. As for closed-form expression
Closed-form expression
In mathematics, an expression is said to be a closed-form expression if it can be expressed analytically in terms of a bounded number of certain "well-known" functions...
s, the criteria are not precisely defined, but the class of expressions considered to be "analytical expressions" tends to be wider.
In particular, special functions
Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications....
such as the Bessel functions and the gamma function
Gamma function
In mathematics, the gamma function is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers...
are usually allowed, and often so are infinite series and continued fraction
Continued fraction
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on...
s. On the other hand, limits
Limit of a sequence
The limit of a sequence is, intuitively, the unique number or point L such that the terms of the sequence become arbitrarily close to L for "large" values of n...
in general, and integral
Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
s in particular, are typically excluded.