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The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...

The system of partial differential equations u_t = (u^2-u_x+2v)_x (1) v_y = (2uv+v_x)_x. (2)

An even Mathieu function ce_r(z,q) with characteristic value a_r.

If f(x) is an even function, then b_n=0 and the Fourier series collapses to f(x)=1/2a_0+sum_(n=1)^inftya_ncos(nx), (1) where a_0 = 1/piint_(-pi)^pif(x)dx (2) = ...

F_x[cos(2pik_0x)](k) = int_(-infty)^inftye^(-2piikx)((e^(2piik_0x)+e^(-2piik_0x))/2)dx (1) = 1/2int_(-infty)^infty[e^(-2pii(k-k_0)x)+e^(-2pii(k+k_0)x)]dx (2) = ...

The function psi(x)={x(1-(x^2)/(c^2))^2 for |x|<c; 0 for |x|>c (1) sometimes used in robust estimation. It has a minimum at x=-c/sqrt(5) and a maximum at x=c/sqrt(5), where ...

The hyperbolic cosecant is defined as cschz=1/(sinhz)=2/(e^z-e^(-z)). (1) It is implemented in the Wolfram Language as Csch[z]. It is related to the hyperbolic cotangent ...

To find the motion of a rectangular membrane with sides of length L_x and L_y (in the absence of gravity), use the two-dimensional wave equation ...

The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric ...

The Mathieu functions are the solutions to the Mathieu differential equation (d^2V)/(dv^2)+[a-2qcos(2v)]V=0. (1) Even solutions are denoted C(a,q,v) and odd solutions by ...