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A root-finding algorithm which converges to a complex root from any starting position. To motivate the formula, consider an nth order polynomial and its derivatives, P_n(x) = ...

A continuous distribution in which the logarithm of a variable has a normal distribution. It is a general case of Gibrat's distribution, to which the log normal distribution ...

The series h_q(-r)=sum_(n=1)^infty1/(q^n+r) (1) for q an integer other than 0 and +/-1. h_q and the related series Ln_q(-r+1)=sum_(n=1)^infty((-1)^n)/(q^n+r), (2) which is a ...

The ABC (atom-bond connectivity) index of a graph is defined as half the sum of the matrix elements of its ABC matrix. It was introduced by Estrada et al. (2017) to model the ...

The natural norm induced by the L-infty-norm is called the maximum absolute row sum norm and is defined by ||A||_infty=max_(i)sum_(j=1)^n|a_(ij)| for a matrix A. This matrix ...

Let p and q be partitions of a positive integer, then there exists a (0,1)-matrix A such that c(A)=p, r(A)=q iff q is dominated by p^*.

A complex vector space is a vector space whose field of scalars is the complex numbers. A linear transformation between complex vector spaces is given by a matrix with ...

A real vector space is a vector space whose field of scalars is the field of reals. A linear transformation between real vector spaces is given by a matrix with real entries ...

A transform which localizes a function both in space and scaling and has some desirable properties compared to the Fourier transform. The transform is based on a wavelet ...

The main diagonal of a square matrix can be extracted in the Wolfram Language using Tr[m, List].