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If, after constructing a difference table, no clear pattern emerges, turn the paper through an angle of 60 degrees and compute a new table. If necessary, repeat the process. ...

Let (a)_i be a sequence of complex numbers and let the lower triangular matrices F=(f)_(nk) and G=(g)_(nk) be defined as f_(nk)=(product_(j=k)^(n-1)(a_j+k))/((n-k)!) and ...

Faà di Bruno's formula gives an explicit equation for the nth derivative of the composition f(g(t)). If f(t) and g(t) are functions for which all necessary derivatives are ...

Let G be group of group order h and D be a set of k elements of G. If the set of differences d_i-d_j contains every nonzero element of G exactly lambda times, then D is a ...

Amazingly, the distribution of a difference of two normally distributed variates X and Y with means and variances (mu_x,sigma_x^2) and (mu_y,sigma_y^2), respectively, is ...

The difference X_1-X_2 of two uniform variates on the interval [0,1] can be found as P_(X_1-X_2)(u) = int_0^1int_0^1delta((x-y)-u)dxdy (1) = 1-u+2uH(-u), (2) where delta(x) ...

Clairaut's difference equation is a special case of Lagrange's equation (Sokolnikoff and Redheffer 1958) defined by u_k=kDeltau_k+F(Deltau_k), (1) or in "x notation," ...

A difference-differential equation is a two-variable equation consisting of a coupled ordinary differential equation and recurrence equation. In older literature, the term ...

Define a power difference prime as a number of the form n^n-(n-1)^(n-1) that is prime. The first few power difference primes then have n=2, 3, 4, 7, 11, 17, 106, 120, 1907, ...

The algorithm of constructing and interpreting a quotient-difference table which allows interconversion of continued fractions, power series, and rational functions ...