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

Q_n^((alpha,beta))(x)=2^(-n-1)(x-1)^(-alpha)(x+1)^(-beta) ×int_(-1)^1(1-t)^(n+alpha)(1+t)^(n+beta)(x-t)^(-n-1)dt. In the exceptional case n=0, alpha+beta+1=0, a nonconstant ...

The wave equation in oblate spheroidal coordinates is del ^2Phi+k^2Phi=partial/(partialxi_1)[(xi_1^2+1)(partialPhi)/(partialxi_1)] ...

The dual vector space to a real vector space V is the vector space of linear functions f:V->R, denoted V^*. In the dual of a complex vector space, the linear functions take ...

A method for fitting a curve (not necessarily a straight line) through a set of points using some goodness-of-fit criterion. The most common type of regression is linear ...

A linear code C is cyclic if for every codeword (c_0,c_1,...,c_(n-1)) in C, the codeword (c_(n-1),c_0,c_1,...,c_(n-2)) is also in C.

The second solution Q_l(x) to the Legendre differential equation. The Legendre functions of the second kind satisfy the same recurrence relation as the Legendre polynomials. ...

A set of orthogonal functions {phi_n(x)} is termed complete in the closed interval x in [a,b] if, for every piecewise continuous function f(x) in the interval, the minimum ...

If X is a normed linear space, then the set of continuous linear functionals on X is called the dual (or conjugate) space of X. When equipped with the norm ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...