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As used in physics, the term "exact" generally refers to a solution that captures the entire physics and mathematics of a problem as opposed to one that is approximate, ...

For a form Q, the generic character chi_i(Q) of Q is defined as the values of chi_i(m) where (m,2d)=1 and Q represents m: chi_1(Q), chi_2(Q), ..., chi_r(Q) (Cohn 1980, p. ...

For a logarithmic spiral given parametrically as x = ae^(bt)cost (1) y = ae^(bt)sint, (2) evolute is given by x_e = -abe^(bt)sint (3) y_e = abe^(bt)cost. (4) As first shown ...

A number of the form n^...^_()_(n)n, where Knuth up-arrow notation has been used. The first few Ackermann numbers are 1^1=1, 2^^2=4, and ...

The Fransén-Robinson constant F is defined by F=int_0^infty(dx)/(Gamma(x))=2.8077702420... (OEIS A058655) where Gamma(x) is the gamma function. No closed-form expression in ...

The Helmholtz differential equation in spherical coordinates is separable. In fact, it is separable under the more general condition that k^2 is of the form ...

A regression that is linear in the unknown parameters used in the fit. The most common form of linear regression is least squares fitting. Least squares fitting of lines and ...

The expansion of the two sides of a sum equality in terms of polynomials in x^m and y^k, followed by closed form summation in terms of x and y. For an example of the ...

The vector triple product identity is also known as the BAC-CAB identity, and can be written in the form Ax(BxC) = B(A·C)-C(A·B) (1) (AxB)xC = -Cx(AxB) (2) = -A(B·C)+B(A·C). ...

A minimal surface and double algebraic surface of 15th order and fifth class which can be given by parametric equations x(u,v) = 2sinhucosv-2/3sinh(3u)cos(3v) (1) y(u,v) = ...