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...

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

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

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...

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

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...

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

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...

mathematics the elliptic rational functions are a sequence of rational functions with real coefficients. Elliptic rational functions are extensively used...

Chebyshev rational functions are a sequence of functions which are both rational and orthogonal. They are named after Pafnuty Chebyshev. A rational Chebyshev...

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

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...

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...

The sheaf of rational functions KX of a scheme X is the generalization to scheme theory of the notion of function field of an algebraic variety in classical...

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

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

branches of the W function without using any iteration. In this method the W function is evaluated as a conditional switch of rational functions on transformed...

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...

Thomae's function is a real-valued function of a real variable that can be defined as:: 531  f ( x ) = { 1 q if  x = p q ( x  is rational), with  p ∈ Z...

a_{m}]} , so the value of the question-mark function on x {\displaystyle x} reduces to the dyadic rational defined by a finite sum, ? ⁡ ( x ) = a 0 + 2...

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...

)}=0,\quad j(i)=1728=12^{3}.} Rational functions of j {\displaystyle j} are modular, and in fact give all modular functions of weight 0. Classically, the...

products compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin or log), as...

In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example...

field of rational functions in one variable over the complex field, since one can prove that any meromorphic function on the sphere is rational. (This is...

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...

Then X has a sheaf of rational functions M X . {\displaystyle {\mathcal {M}}_{X}.} All regular functions are rational functions, which leads to a short...

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...

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

\mathbb {C} \smallsetminus \{0\}} ⁠. (The reciprocal function, and any other rational function, is meromorphic on ⁠ C {\displaystyle \mathbb {C} } ⁠...