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The constant a_(-1) in the Laurent series f(z)=sum_(n=-infty)^inftya_n(z-z_0)^n (1) of f(z) about a point z_0 is called the residue of f(z). If f is analytic at z_0, its ...

A method of computing the determinant of a square matrix due to Charles Dodgson (1866) (who is more famous under his pseudonym Lewis Carroll). The method is useful for hand ...

Find a square number x^2 such that, when a given integer h is added or subtracted, new square numbers are obtained so that x^2+h=a^2 (1) and x^2-h=b^2. (2) This problem was ...

Contour integration is the process of calculating the values of a contour integral around a given contour in the complex plane. As a result of a truly amazing property of ...

The first few terms of the continued fraction of the Copeland-Erdős constant are [0; 4, 4, 8, 16, 18, 5, 1, ...] (OEIS A030168), illustrated above. Interestingly, while the ...

The most common form of cosine integral is Ci(x) = -int_x^infty(costdt)/t (1) = gamma+lnx+int_0^x(cost-1)/tdt (2) = 1/2[Ei(ix)+Ei(-ix)] (3) = -1/2[E_1(ix)+E_1(-ix)], (4) ...

The Coulomb wave function is a special case of the confluent hypergeometric function of the first kind. It gives the solution to the radial Schrödinger equation in the ...

Covariance provides a measure of the strength of the correlation between two or more sets of random variates. The covariance for two random variates X and Y, each with sample ...

A number of attractive cube 6-compounds can be constructed. A first (left figures) is obtained by combining six cubes, each rotated by 1/6 of a turn about the line joining ...

A cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of m control points. The second derivative of each polynomial is commonly ...