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A test for the convergence of Fourier series. Let phi_x(t)=f(x+t)+f(x-t)-2f(x), then if int_0^pi(|phi_x(t)|dt)/t is finite, the Fourier series converges to f(x) at x.

If (f,U) and (g,V) are functions elements, then (g,V) is a direct analytic continuation of (f,U) if U intersection V!=emptyset and f and g are equal on U intersection V.

In general, an integer n is divisible by d iff the digit sum s_(d+1)(n) is divisible by d. Write a positive decimal integer a out digit by digit in the form ...

Consider the family of ellipses (x^2)/(c^2)+(y^2)/((1-c)^2)-1=0 (1) for c in [0,1]. The partial derivative with respect to c is -(2x^2)/(c^3)+(2y^2)/((1-c)^3)=0 (2) ...

A factorization algorithm which works by expressing N as a quadratic form in two different ways. Then N=a^2+b^2=c^2+d^2, (1) so a^2-c^2=d^2-b^2 (2) (a-c)(a+c)=(d-b)(d+b). (3) ...

Donaldson (1983) showed there exists an exotic smooth differential structure on R^4. Donaldson's result has been extended to there being precisely a continuum of ...

Any nondegenerate closed space curve may be nondegenerately deformed into either of the two curves illustrated above. Neither of these can be nondegenerately transformed into ...

The first isodynamic point S has triangle center function alpha_(15)=sin(A+1/3pi) and is Kimberling center X_(15) (Kimberling 1998, p. 68).

A set in R^d formed by translating an affine subspace or by the intersection of a set of hyperplanes.

The dual of the uniform great rhombicuboctahedron and Wenninger dual W_(85).