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An alternative name for an associated Legendre polynomial.

The Walsh functions consist of trains of square pulses (with the allowed states being -1 and 1) such that transitions may only occur at fixed intervals of a unit time step, ...

Toroidal functions are a class of functions also called ring functions that appear in systems having toroidal symmetry. Toroidal functions can be expressed in terms of the ...

The computer animation format MPEG-7 uses Gabor functions to specify texture descriptors.

The Glaisher-Kinkelin constant A is defined by lim_(n->infty)(H(n))/(n^(n^2/2+n/2+1/12)e^(-n^2/4))=A (1) (Glaisher 1878, 1894, Voros 1987), where H(n) is the hyperfactorial, ...

Affine functions represent vector-valued functions of the form f(x_1,...,x_n)=A_1x_1+...+A_nx_n+b. The coefficients can be scalars or dense or sparse matrices. The constant ...

The Mathieu functions are the solutions to the Mathieu differential equation (d^2V)/(dv^2)+[a-2qcos(2v)]V=0. (1) Even solutions are denoted C(a,q,v) and odd solutions by ...

F_k[P_N(k)](x)=F_k[exp(-N|k|^beta)](x), where F is the Fourier transform of the probability P_N(k) for N-step addition of random variables. Lévy showed that beta in (0,2) for ...

The parabolic cylinder functions are a class of functions sometimes called Weber functions. There are a number of slightly different definitions in use by various authors. ...

Elliptic rational functions R_n(xi,x) are a special class of rational functions that have nice properties for approximating other functions over the interval x in [-1,1]. In ...