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Let z=re^(itheta)=x+iy be a complex number, then inequality |(zexp(sqrt(1-z^2)))/(1+sqrt(1-z^2))|<=1 (1) holds in the lens-shaped region illustrated above. Written explicitly ...

There are two sets of constants that are commonly known as Lebesgue constants. The first is related to approximation of function via Fourier series, which the other arises in ...

The Owen T-function is defined as T(x,a)=1/(2pi)int_0^a(e^(-x^2(1+t^2)/2))/(1+t^2)dt. It is implemented in the Wolfram Language as OwenT[x, a]. A special value is given by ...

A homogeneous polynomial in two or more variables.

The ring R[x] of polynomials in a variable x.

A sequence of polynomials p_i(x), for i=0, 1, 2, ..., where p_i(x) is exactly of degree i for all i.

The relationship x precedes y is written x≺y. The relation x precedes or is equal to y is written x<=y.

An algorithm which finds the least nonnegative value of sqrt(a (mod p)) for given a and prime p.

A congruence that has a solution.

Picking two independent sets of points x and y from a unit uniform distribution and placing them at coordinates (x,y) gives points uniformly distributed over the unit square. ...