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Because the Legendre polynomials form a complete orthogonal system over the interval [-1,1] with respect to the weighting function w(x)=1, any function f(x) may be expanded ...

The maximum possible weight of a fractional clique of a graph G is called the fractional clique number of G, denoted omega^*(G) (Godsil and Royle 2001, pp. 136-137) or ...

For any nonzero lambda in C, either 1. The equation Tv-lambdav=0 has a nonzero solution v, or 2. The equation Tv-lambdav=f has a unique solution v for any function f. In the ...

Let X and Y be Banach spaces and let f:X->Y be a function between them. f is said to be Gâteaux differentiable if there exists an operator T_x:X->Y such that, for all v in X, ...

There are two camps of thought on the meaning of general recursive function. One camp considers general recursive functions to be equivalent to the usual recursive functions. ...

The Gibbs phenomenon is an overshoot (or "ringing") of Fourier series and other eigenfunction series occurring at simple discontinuities. It can be reduced with the Lanczos ...

The granny knot is a composite knot of six crossings consisting of a knot sum of two left-handed trefoils with the same orientation (Rolfsen 1976, p. 220). The granny knot ...

The grid shading problem is the problem of proving the unimodality of the sequence {a_1,a_2,...,a_(mn)}, where for fixed m and n, a_i is the number of partitions of i with at ...

Let n be an integer such that n>=lambda_1, where lambda=(lambda_1,lambda_2,...) is a partition of n=|lambda| if lambda_1>=lambda_2>=...>=0, where lambda_i are a sequence of ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), define the Hilbert function of M as the map ...