In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator...

asymptote is the case of a rational function at a point x such that the denominator is zero and the numerator is non-zero. If a function has a vertical asymptote...

confusion between "rational expression" and "rational function" (a polynomial is a rational expression and defines a rational function, even if its coefficients...

modeling), polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting. A polynomial function is one that has...

mathematics, the Dirichlet function is the indicator function 1 Q {\displaystyle \mathbf {1} _{\mathbb {Q} }} of the set of rational numbers Q {\displaystyle...

rewritten as a rational fraction is a rational function. While polynomial functions are defined for all values of the variables, a rational function is defined...

procedure results in families of rational orthogonal functions called Legendre rational functions and Chebyshev rational functions. Solutions of linear differential...

other x-coordinate. The function f ( x ) = { 1 x  rational  0 x  irrational  {\displaystyle f(x)={\begin{cases}1&x{\text{ rational }}\\0&x{\text{ irrational...

any product wherein each factor is a rational function of the index variable, by factoring the rational function into linear expressions. If P and Q are...

include constant functions, linear functions and quadratic functions. Rational functions are quotients of two polynomial functions, and their domain...

example of a homogeneous function of degree k is the function defined by a homogeneous polynomial of degree k. The rational function defined by the quotient...

functions) of rational functions. Any rational function can be integrated by partial fraction decomposition of the function into a sum of functions of...

any rational function on the complex plane can be extended to a holomorphic function on the Riemann sphere, with the poles of the rational function mapping...

all 1 ≤ i ≤ ℓ. In general, Hadamard products of rational functions produce rational generating functions. Similarly, if F ( s , t ) := ∑ m , n ≥ 0 f ( m...

function from the Riemann sphere onto itself. Such functions f ( z ) {\displaystyle f(z)} are precisely the non-constant complex rational functions,...

ratio of two integers Rational point of an algebraic variety, a point defined over the rational numbers Rational function, a function that may be defined...

algebraic number theory, such as the field of rational numbers, number fields, finite fields, function fields, and p-adic fields. A large part of singularity...

means that its function field is isomorphic to K ( U 1 , … , U d ) , {\displaystyle K(U_{1},\dots ,U_{d}),} the field of all rational functions for some set...

holomorphic except at certain isolated poles), resembles a rational fraction ("part") of entire functions in a domain of the complex plane. Cauchy had instead...

integrals, which converts a rational function of trigonometric functions of x {\textstyle x} into an ordinary rational function of t {\textstyle t} by setting...

field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as fields of rational functions, algebraic...

Note that not every complex number in A needs to be a pole of every rational function of the sequence ( r n ) n ∈ N {\displaystyle (r_{n})_{n\in \mathbb...

Simple examples of algebraic functions are the rational functions and the square root function, but in general, algebraic functions cannot be defined as finite...

An infinite series of any rational function of n{\displaystyle n} can be reduced to a finite series of polygamma functions, by use of partial fraction...

integral domain), is called the field of rational functions, field of rational fractions, or field of rational expressions and is denoted K ( X ) {\displaystyle...

formula supplies the necessary correction terms. The function ez is not in the rational function ring C ( z ) {\displaystyle \mathbb {C} (z)} : it is...

Rational choice theory refers to a set of guidelines that help understand economic and social behaviour. The theory originated in the eighteenth century...

particular the subfield of algebraic geometry, a rational map or rational mapping is a kind of partial function between algebraic varieties. This article uses...

functions defined on the real algebraic variety x2 + y2 = −1 is a field of genus zero which is not a rational function field. Concretely, a rational curve...

development of the logarithm and, in fact, the so-defined zeta function is a rational function in T: Z ( E ( F p ) , T ) = 1 − a p T + p T 2 ( 1 − T ) ( 1...