mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f {\displaystyle f} , is a member x {\displaystyle...

a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a...

called zero elements.) Examples include identity elements of additive groups and vector spaces. Another example is the zero function (or zero map) on a domain...

singularity of such a function (see essential singularity). Technically, a point z0 is a pole of a function f if it is a zero of the function 1/f and 1/f...

contained the Riemann hypothesis, a conjecture about the distribution of complex zeros of the Riemann zeta function that many mathematicians consider...

The law of trichotomy states that every real number must be positive, negative or zero. The signum function denotes which unique category a number falls...

analysis, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f is a number x...

A zero-crossing is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis...

that is, a polynomial function of degree zero or one. For distinguishing such a linear function from the other concept, the term affine function is often...

Unsolved problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part of one half? More unsolved problems in mathematics...

{\displaystyle X} is a real-valued function with only some of the properties of a seminorm. Unlike seminorms, a sublinear function does not have to be...

mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the...

Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value is zero everywhere...

statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen...

support of a real-valued function f {\displaystyle f} is the subset of the function domain of elements that are not mapped to zero. If the domain of f {\displaystyle...

is an absorbing element under Cartesian product of sets, since { } × S = { } The zero function or zero map defined by z(x) = 0 under pointwise multiplication...

function is zero Zero (complex analysis), a zero of a holomorphic function Zero element, generalization of the number zero in algebraic structures Zero object...

quadratic function is a parabola. If a quadratic function is equated with zero, then the result is a quadratic equation. The solutions of a quadratic equation...

Every coefficient of the Taylor expansion around x = 0 is exactly zero, but the function is non-zero if x ≠ 0. In physics, such functions arise for phenomena...

function of the first kind is an entire function if α is an integer, otherwise it is a multivalued function with singularity at zero. The graphs of Bessel...

tends to some value. When a real function can be expressed as a fraction whose denominator tends to zero, the output of the function becomes arbitrarily large...

Zero to the power of zero, denoted as 0 0 {\displaystyle {\boldsymbol {0^{0}}}} , is a mathematical expression with different interpretations depending...

– Mertens function zero 2095 – Mertens function zero 2096 – Mertens function zero 2097 – Mertens function zero 2099 – Mertens function zero, super-prime...

holomorphic except at zero and the negative integers, where it has simple poles. The gamma function has no zeros, so the reciprocal gamma function ⁠1/Γ(z)⁠ is an...

scaling of the independent variable (the x axis) by a factor of π. In both cases, the value of the function at the removable singularity at zero is understood...

incomplete gamma function, which is defined as an integral from zero to a variable upper limit. Similarly, the upper incomplete gamma function is defined as...

{\displaystyle \theta =\pi n} . This is a consequence of the identities of these functions, which would imply a division by zero at those points. Also, arcsin ⁡...

raising to the power of a positive integer. Constant function: polynomial of degree zero, graph is a horizontal straight line Linear function: First degree polynomial...

analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions...

continuous function f, an interval [a, b], and the function values f(a) and f(b). The function values are of opposite sign (there is at least one zero crossing...