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A convolution is an integral that expresses the amount of overlap of one function g as it is shifted over another function f. It therefore "blends" one function with another. ...

The correlation coefficient, sometimes also called the cross-correlation coefficient, Pearson correlation coefficient (PCC), Pearson's r, the Perason product-moment ...

There are no fewer than three distinct notions of curve throughout mathematics. In topology, a curve is a one-dimensional continuum (Charatonik and Prajs 2001). In algebraic ...

The Dirichlet beta function is defined by the sum beta(x) = sum_(n=0)^(infty)(-1)^n(2n+1)^(-x) (1) = 2^(-x)Phi(-1,x,1/2), (2) where Phi(z,s,a) is the Lerch transcendent. The ...

The Dirichlet eta function is the function eta(s) defined by eta(s) = sum_(k=1)^(infty)((-1)^(k-1))/(k^s) (1) = (1-2^(1-s))zeta(s), (2) where zeta(s) is the Riemann zeta ...

The distance between two points is the length of the path connecting them. In the plane, the distance between points (x_1,y_1) and (x_2,y_2) is given by the Pythagorean ...

All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately ...

Elder's theorem is a generalization of Stanley's theorem which states that the total number of occurrences of an integer k among all unordered partitions of n is equal to the ...

The classic treatise in geometry written by Euclid and used as a textbook for more than 1000 years in western Europe. An Arabic version The Elements appears at the end of the ...

The Epstein zeta function for a n×n matrix S of a positive definite real quadratic form and rho a complex variable with R[rho]>n/2 (where R[z] denotes the real part) is ...