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If (1+xsin^2alpha)sinbeta=(1+x)sinalpha, then (1+x)int_0^alpha(dphi)/(sqrt(1-x^2sin^2phi))=int_0^beta(dphi)/(sqrt(1-(4x)/((1+x)^2)sin^2phi)).

An algorithm for computing an Egyptian fraction.

The head of a vector AB^-> is the endpoint B, i.e., the point at which the arrow is placed.

A fixed point for which the stability matrix has equal nonzero eigenvectors.

A spherical image of a curve. The most common indicatrix is Dupin's indicatrix.

A polynomial in which the sum of subscripts is the same in each term.

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

The quantities obtained from cubic, hexagonal, etc., lattice sums, evaluated at s=1, are called Madelung constants. For cubic lattice sums ...

Mills (1947) proved the existence of a real constant A such that |_A^(3^n)_| (1) is prime for all integers n>=1, where |_x_| is the floor function. Mills (1947) did not, ...

The appropriate notion of integer for surreal numbers.