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There are six Painlevé transcendents, corresponding to second-order ordinary differential equations whose only movable singularities are ordinary poles and which cannot be ...

The wave equation in prolate spheroidal coordinates is del ...

A square pyramid is a pyramid with a square base. It is a pentahedron. The lateral edge length e and slant height s of a right square pyramid of side length a and height h ...

A hyperboloid is a quadratic surface which may be one- or two-sheeted. The two-sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the line ...

Ellipsoidal harmonics of the second kind, also known as Lamé functions of the second kind, are variously defined as F_m^p(x)=(2m+1)E_m^p(x) ...

Informally, an L^2-function is a function f:X->R that is square integrable, i.e., |f|^2=int_X|f|^2dmu with respect to the measure mu, exists (and is finite), in which case ...

An orthodiagonal quadrangle is a quadrangle whose diagonals are perpendicular to each other. If a, b, c, and d are the sides of a quadrangle, then this quadrangle is ...

Define the notation [n]f_0=f_(-(n-1)/2)+...+f_0+...+f_((n-1)/2) (1) and let delta be the central difference, so delta^2f_0=f_1-2f_0+f_(-1). (2) Spencer's 21-term moving ...

The duplication formula for Rogers L-function follows from Abel's functional equation and is given by 1/2L(x^2)=L(x)-L(x/(1+x)).

There are two definitions of the Fermat number. The less common is a number of the form 2^n+1 obtained by setting x=1 in a Fermat polynomial, the first few of which are 3, 5, ...