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An iterated map is a map that is applied repeatedly to an object. The Wolfram Language function NestList[f, expr, n] gives a list of the results of iterating the function f n ...

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

A distribution of error such that the error remaining is always given approximately by the last term dropped.

Legendre and Whittaker and Watson's (1990) term for the beta integral int_0^1x^p(1-x)^qdx, whose solution is the beta function B(p+1,q+1).

For R[n]>-1 and R[z]>0, Pi(z,n) = n^zint_0^1(1-x)^nx^(z-1)dx (1) = (n!)/((z)_(n+1))n^z (2) = B(z,n+1), (3) where (z)_n is the Pochhammer symbol and B(p,q) is the beta ...

Orthogonal polynomials are classes of polynomials {p_n(x)} defined over a range [a,b] that obey an orthogonality relation int_a^bw(x)p_m(x)p_n(x)dx=delta_(mn)c_n, (1) where ...

A special case of Hölder's sum inequality with p=q=2, (sum_(k=1)^na_kb_k)^2<=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2), (1) where equality holds for a_k=cb_k. The inequality is ...

A class of formal series expansions in derivatives of a distribution Psi(t) which may (but need not) be the normal distribution function Phi(t)=1/(sqrt(2pi))e^(-t^2/2) (1) ...

The detour polynomial of a graph G is the characteristic polynomial of the detour matrix of G. Precomputed detour polynomials for many named graphs are available in the ...

For n a positive integer, expressions of the form sin(nx), cos(nx), and tan(nx) can be expressed in terms of sinx and cosx only using the Euler formula and binomial theorem. ...