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For R[z]>0, where J_nu(z) is a Bessel function of the first kind.

A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one ...

The term "quotient" is most commonly used to refer to the ratio q=r/s of two quantities r and s, where s!=0. Less commonly, the term quotient is also used to mean the integer ...

A metric space is a set S with a global distance function (the metric g) that, for every two points x,y in S, gives the distance between them as a nonnegative real number ...

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of ...

Three elements x, y and z of a set S are said to be associative under a binary operation * if they satisfy x*(y*z)=(x*y)*z. (1) Real numbers are associative under addition ...

Two elements x and y of a set S are said to be commutative under a binary operation * if they satisfy x*y=y*x. (1) Real numbers are commutative under addition x+y=y+x (2) and ...

Let R+B be the number of monochromatic forced triangles (where R and B are the number of red and blue triangles) in an extremal graph. Then R+B=(n; 3)-|_1/2n|_1/4(n-1)^2_|_|, ...

Let S be a mathematical statement, then the Iverson bracket is defined by [S]={0 if S is false; 1 if S is true, (1) and corresponds to the so-called characteristic function. ...

Let L(x) denote the Rogers L-function defined in terms of the usual dilogarithm by L(x) = 6/(pi^2)[Li_2(x)+1/2lnxln(1-x)] (1) = ...