Search Results for ""

A constant function is function f(x)=c whose value does not change as its parameters vary. The function graph of a one-dimensional constant function is a straight line. The ...

A family of operators mapping each space M_k of modular forms onto itself. For a fixed integer k and any positive integer n, the Hecke operator T_n is defined on the set M_k ...

In 1979, Conway and Norton discovered an unexpected intimate connection between the monster group M and the j-function. The Fourier expansion of j(tau) is given by (1) (OEIS ...

Let f(x) be integrable in [-1,1], let (1-x^2)f(x) be of bounded variation in [-1,1], let M^' denote the least upper bound of |f(x)(1-x^2)| in [-1,1], and let V^' denote the ...

The ramp function is defined by R(x) = xH(x) (1) = int_(-infty)^xH(x^')dx^' (2) = int_(-infty)^inftyH(x^')H(x-x^')dx^' (3) = H(x)*H(x), (4) where H(x) is the Heaviside step ...

Analytic representations the symmetric triangle wave with period 2 and varying between -1 and 1 include f(x) = 2/pisin^(-1)[sin(pix)] (1) = 1-2|1-[2(1/2x+1/4 (mod 1))]| (2) = ...

A method to obtain a signal C_l(z) with a flat spectrum c(theta;z) (such as a pulse), but having a smaller amplitude than the pulse. ...

There are a number of functions in various branches of mathematics known as Riemann functions. Examples include the Riemann P-series, Riemann-Siegel functions, Riemann theta ...

The class of continuous functions is called the Baire class 0. For each n, the functions that can be considered as pointwise limits of sequences of functions of Baire class ...

A cusp form is a modular form for which the coefficient c(0)=0 in the Fourier series f(tau)=sum_(n=0)^inftyc(n)e^(2piintau) (1) (Apostol 1997, p. 114). The only entire cusp ...