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Some interesting properties (as well as a few arcane ones not reiterated here) of the number 239 are discussed in Schroeppel (1972). 239 appears in Machin's formula ...

The central difference for a function tabulated at equal intervals f_n is defined by delta(f_n)=delta_n=delta_n^1=f_(n+1/2)-f_(n-1/2). (1) First and higher order central ...

The nth central fibonomial coefficient is defined as [2n; n]_F = product_(k=1)^(n)(F_(n+k))/(F_k) (1) = ...

A cubic triangular number is a positive integer that is simultaneously cubic and triangular. Such a number must therefore satisfy T_n=m^3 for some positive integers n and m, ...

Given a hereditary representation of a number n in base b, let B[b](n) be the nonnegative integer which results if we syntactically replace each b by b+1 (i.e., B[b] is a ...

If p_1, ..., p_n are positive numbers which sum to 1 and f is a real continuous function that is convex, then f(sum_(i=1)^np_ix_i)<=sum_(i=1)^np_if(x_i). (1) If f is concave, ...

The expected number of real zeros E_n of a random polynomial of degree n if the coefficients are independent and distributed normally is given by E_n = ...

The group Gamma of all Möbius transformations of the form tau^'=(atau+b)/(ctau+d), (1) where a, b, c, and d are integers with ad-bc=1. The group can be represented by the 2×2 ...

If p is a prime >3, then the numerator of the harmonic number H_(p-1)=1+1/2+1/3+...+1/(p-1) (1) is divisible by p^2 and the numerator of the generalized harmonic number ...

The d-analog of a complex number s is defined as [s]_d=1-(2^d)/(s^d) (1) (Flajolet et al. 1995). For integer n, [2]!=1 and [n]_d! = [3][4]...[n] (2) = ...