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A curious approximation to the Feigenbaum constant delta is given by pi+tan^(-1)(e^pi)=4.669201932..., (1) where e^pi is Gelfond's constant, which is good to 6 digits to the ...

The ratio C of the largest to smallest singular value in the singular value decomposition of a matrix. The base-b logarithm of C is an estimate of how many base-b digits are ...

A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. The ...

A special function mostly commonly denoted psi_n(z), psi^((n))(z), or F_n(z-1) which is given by the (n+1)st derivative of the logarithm of the gamma function Gamma(z) (or, ...

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 Pierce expansion, or alternated Egyptian product, of a real number 0<x<1 is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

Let P be the principal (initial investment), r be the annual compounded rate, i^((n)) the "nominal rate," n be the number of times interest is compounded per year (i.e., 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 ...

Let S(x) denote the number of positive integers not exceeding x which can be expressed as a sum of two squares (i.e., those n<=x such that the sum of squares function ...

A function built up of a finite combination of constant functions, field operations (addition, multiplication, division, and root extractions--the elementary operations)--and ...