Search Results for ""

A number t_x=tan^(-1)(1/x)=cot^(-1)x, where x is an integer or rational number, tan^(-1)x is the inverse tangent, and cot^(-1)x is the inverse cotangent. Gregory numbers ...

Expresses a function in terms of its Radon transform, f(x,y) = R^(-1)(Rf)(x,y) (1) = ...

cos(pi/(10)) = 1/4sqrt(10+2sqrt(5)) (1) cos((3pi)/(10)) = 1/4sqrt(10-2sqrt(5)) (2) cot(pi/(10)) = sqrt(5+2sqrt(5)) (3) cot((3pi)/(10)) = sqrt(5-2sqrt(5)) (4) csc(pi/(10)) = ...

cos(pi/8) = 1/2sqrt(2+sqrt(2)) (1) cos((3pi)/8) = 1/2sqrt(2-sqrt(2)) (2) cot(pi/8) = 1+sqrt(2) (3) cot((3pi)/8) = sqrt(2)-1 (4) csc(pi/8) = sqrt(4+2sqrt(2)) (5) csc((3pi)/8) ...

The Jacobi theta functions are the elliptic analogs of the exponential function, and may be used to express the Jacobi elliptic functions. The theta functions are ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

Watson (1939) considered the following three triple integrals, I_1 = 1/(pi^3)int_0^piint_0^piint_0^pi(dudvdw)/(1-cosucosvcosw) (1) = (4[K(1/2sqrt(2))]^2)/(pi^2) (2) = ...

The radius of an excircle. Let a triangle have exradius r_A (sometimes denoted rho_A), opposite side of length a and angle A, area Delta, and semiperimeter s. Then r_1 = ...

It is always possible to write a sum of sinusoidal functions f(theta)=acostheta+bsintheta (1) as a single sinusoid the form f(theta)=ccos(theta+delta). (2) This can be done ...

A differential k-form is a tensor of tensor rank k that is antisymmetric under exchange of any pair of indices. The number of algebraically independent components in n ...