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Let sopfr(n) be the sum of prime factors (with repetition) of a number n. For example, 20=2^2·5, so sopfr(20)=2+2+5=9. Then sopfr(n) for n=1, 2, ... is given by 0, 2, 3, 4, ...

The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by x = ...

The base 16 notational system for representing real numbers. The digits used to represent numbers using hexadecimal notation are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, ...

Analytic continuation (sometimes called simply "continuation") provides a way of extending the domain over which a complex function is defined. The most common application is ...

A permutation cycle is a subset of a permutation whose elements trade places with one another. Permutations cycles are called "orbits" by Comtet (1974, p. 256). For example, ...

The Mittag-Leffler function (Mittag-Leffler 1903, 1905) is an entire function defined by the series E_alpha(z)=sum_(k=0)^infty(z^k)/(Gamma(alphak+1)) (1) for alpha>0. It is ...

The log-series distribution, also sometimes called the logarithmic distribution (although this work reserves that term for a distinct distribution), is the distribution of ...

A branch point of an analytic function is a point in the complex plane whose complex argument can be mapped from a single point in the domain to multiple points in the range. ...

For all integers n and nonnegative integers t, the harmonic logarithms lambda_n^((t))(x) of order t and degree n are defined as the unique functions satisfying 1. ...

Suppose that V is a group representation of G, and W is a group representation of H. Then the vector space tensor product V tensor W is a group representation of the group ...