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The term "left factorial" is sometimes used to refer to the subfactorial !n, the first few values for n=1, 2, ... are 1, 3, 9, 33, 153, 873, 5913, ... (OEIS A007489). ...

The Legendre transform of a sequence {c_k} is the sequence {a_k} with terms given by a_n = sum_(k=0)^(n)(n; k)(n+k; k)c_k (1) = sum_(k=0)^(n)(2k; k)(n+k; n-k)c_k, (2) where ...

A quantity used to test nested hypotheses. Let H^' be a nested hypothesis with n^' degrees of freedom within H (which has n degrees of freedom), then calculate the maximum ...

If the random variates X_1, X_2, ... satisfy the Lindeberg condition, then for all a<b, lim_(n->infty)P(a<(S_n)/(s_n)<b)=Phi(b)-Phi(a), where Phi is the normal distribution ...

A linear extension of a partially ordered set P is a permutation of the elements p_1, p_2, ... of P such that p_i<p_j implies i<j. For example, the linear extensions of the ...

The symbol o(x), pronounced "little-O of x," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function. In particular, if n ...

There are two nonintersecting circles that are tangent to all three Lucas circles. (These are therefore the Soddy circles of the Lucas central triangle.) The inner one, ...

When P and Q are integers such that D=P^2-4Q!=0, define the Lucas sequence {U_k} by U_k=(a^k-b^k)/(a-b) for k>=0, with a and b the two roots of x^2-Px+Q=0. Then define a ...

A triangle center alpha:beta:gamma is called a major triangle center if the triangle center function alpha=f(a,b,c,A,B,C) is a function of angle A alone, and therefore beta ...

The inconic having inconic parameters x:y:z=a/(b+c-a):b/(a+c-b):c/(a+b-c). Its center is the mittenpunkt M of the triangle and its Brianchon point is the Nagel point Na. The ...