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A Padé approximant perturbed with a Chebyshev polynomial of the first kind to reduce the leading coefficient in the error.

Using a Chebyshev polynomial of the first kind T(x), define c_j = 2/Nsum_(k=1)^(N)f(x_k)T_j(x_k) (1) = 2/Nsum_(k=1)^(N)f[cos{(pi(k-1/2))/N}]cos{(pij(k-1/2))/N}. (2) Then f(x) ...

If theta is a given irrational number, then the sequence of numbers {ntheta}, where {x}=x-|_x_|, is dense in the unit interval. Explicitly, given any alpha, 0<=alpha<=1, and ...

For any algebraic number x of degree n>2, a rational approximation p/q to x must satisfy |x-p/q|>1/(q^n) for sufficiently large q. Writing r=n leads to the definition of the ...

A Banach space X has the approximation property (AP) if, for every epsilon>0 and each compact subset K of X, there is a finite rank operator T in X such that for each x in K, ...

A full angle, also called a complete angle, round angle, or perigon, is an angle equal to 2pi radians =360 degrees corresponding to the central angle of an entire circle. ...

Let X and Y be CW-complexes, and let f:X->Y be a continuous map. Then the cellular approximation theorem states that any such f is homotopic to a cellular map. In fact, if ...

If X is any space, then there is a CW-complex Y and a map f:Y->X inducing isomorphisms on all homotopy, homology, and cohomology groups.

A reflex angle is an angle of more than 180 degrees. A full angle is therefore a reflex angle, while acute, obtuse, right, and straight angles are not.

A straight angle is an angle equal to 180 degrees=pi radians. Two right angles make a straight angle, and two straight angles make a full angle.