Search Results for ""

Given a set of linear equations {a_1x+b_1y+c_1z=d_1; a_2x+b_2y+c_2z=d_2; a_3x+b_3y+c_3z=d_3, (1) consider the determinant D=|a_1 b_1 c_1; a_2 b_2 c_2; a_3 b_3 c_3|. (2) Now ...

A coordinate system defined by the transformation equations x = a/Lambdacnmucnnucospsi (1) y = a/Lambdacnmucnnusinpsi (2) z = a/Lambdasnmudnmusnnudnnu, (3) where ...

Define I_n=(-1)^nint_0^infty(lnz)^ne^(-z)dz, (1) then I_n=(-1)^nGamma^((n))(1), (2) where Gamma^((n))(z) is the nth derivative of the gamma function. Particular values ...

The Hadamard product is a representation for the Riemann zeta function zeta(s) as a product over its nontrivial zeros rho, ...

The case of the Weierstrass elliptic function with invariants g_2=-1 and g_3=0. The half-periods for this case are L(1+i)/4 and L(-1+i)/4, where L is the lemniscate constant ...

The generalized law of sines applies to a simplex in space of any dimension with constant Gaussian curvature. Let us work up to that. Initially in two-dimensional space, we ...

The Engel expansion, also called the Egyptian product, of a positive real number x is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

An arithmetic progression, also known as an arithmetic sequence, is a sequence of n numbers {a_0+kd}_(k=0)^(n-1) such that the differences between successive terms is a ...

There exists an absolute constant C such that for any positive integer m, the discrepancy of any sequence {alpha_n} satisfies ...

A function of the coordinates which is constant along a trajectory in phase space. The number of degrees of freedom of a dynamical system such as the Duffing differential ...