function without zeros
1Gamma function — For the gamma function of ordinals, see Veblen function. The gamma function along part of the real axis In mathematics, the gamma function (represented by the capital Greek letter Γ) is an extension of the factorial function, with its… …
2Dirichlet eta function — For the modular form see Dedekind eta function. Dirichlet eta function η(s) in the complex plane. The color of a point s encodes the value of η(s). Strong colors denote values close to zero and hue encodes the value s argumen …
3Z function — In mathematics, the Z function is a function used for studying the Riemann zeta function along the critical line where the real part of the argument is one half. It is also called the Riemann Siegel Z function, the Riemann Siegel zeta function,… …
4Zeta function universality — In mathematics, the universality of zeta functions is the remarkable property of the Riemann zeta function and other, similar, functions, such as the Dirichlet L functions, to approximate arbitrary non vanishing holomorphic functions arbitrarily… …
5Algebraic function — In mathematics, an algebraic function is informally a function which satisfies a polynomial equation whose coefficients are themselves polynomials. For example, an algebraic function in one variable x is a solution y for an equation: a n(x)y^n+a… …
6Chebyshev function — The Chebyshev function ψ(x), with x < 50 The function ψ( …
7Riemann zeta function — ▪ mathematics function useful in number theory for investigating properties of prime numbers (prime). Written as ζ(x), it was originally defined as the infinite series ζ(x) = 1 + 2−x + 3−x + 4−x + ⋯. When x = 1, this series is called the… …
8Bessel function — In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel s differential equation: for an arbitrary real or complex number α (the order of the …
9Cubic function — This article is about cubic equations in one variable. For cubic equations in two variables, see elliptic curve. Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis where y = 0). It has 2 critical points. Here …
10Auxiliary function — In mathematics, auxiliary functions are an important construction in transcendental number theory. They are functions which appear in most proofs in this area of mathematics and that have specific, desirable properties, such as taking the value… …
