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All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.

The use of permil (a.k.a. parts per thousand) is a way of expressing ratios in terms of whole numbers. Given a ratio or fraction, it is converted to a permil-age by ...

The permutohedron is the n-dimensional generalization of the hexagon. The n-permutohedron is the convex hull of all permutations of the vector (x_1,x_2,...,x_(n+1)) in ...

The "perp dot product" a^_|_·b for a and b vectors in the plane is a modification of the two-dimensional dot product in which a is replaced by the perpendicular vector ...

The integer sequence defined by the recurrence P(n)=P(n-2)+P(n-3) (1) with the initial conditions P(0)=3, P(1)=0, P(2)=2. This recurrence relation is the same as that for the ...

If all elements a_(ij) of an irreducible matrix A are nonnegative, then R=minM_lambda is an eigenvalue of A and all the eigenvalues of A lie on the disk |z|<=R, where, if ...

int_0^z(t^mu)/(1+t)dt=z/(mu+1+((mu+1)^2z)/((mu+2)-(mu+1)z+((mu+2)^2z)/((mu+3)-(mu+2)z+...))) for mu>-1 and -1<z<=1 (Perron 1954-1957, p. 18; Borwein et al. 2004, p. 35).

A^*(x)=sum_(lambda_n<=x)^'a_n=1/(2pii)int_(c-iinfty)^(c+iinfty)f(s)(e^(sx))/sds, where f(s)=suma_ne^(-lambda_ns).

If mu=(mu_1,mu_2,...,mu_n) is an arbitrary set of positive numbers, then all eigenvalues lambda of the n×n matrix a=a_(ij) lie on the disk |z|<=m_mu, where ...

The line joining the three collinear points of intersection of the extensions of corresponding sides in perspective triangles, also called the perspectrix or homology axis.