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If P(n) is a sentential formula depending on a variable n ranging in a set of real numbers, the sentence P(n) for every sufficiently large n (1) means exists N such that P(n) ...

The orthogonal polynomials defined variously by (1) (Koekoek and Swarttouw 1998, p. 24) or p_n(x;a,b,c,d) = W_n(-x^2;a,b,c,d) (2) = (3) (Koepf, p. 116, 1998). The first few ...

For a connection A and a positive spinor phi in Gamma(V_+), Witten's equations (also called the Seiberg-Witten invariants) are given by D_Aphi = 0 (1) F_+^A = ...

A tensor t is said to satisfy the double contraction relation when t_(ij)^m^_t_(ij)^n=delta_(mn). (1) This equation is satisfied by t^^^0 = (2z^^z^^-x^^x^^-y^^y^^)/(sqrt(6)) ...

A hexagrammic prism is a prism formed by two regular hexagrams offset along their symmetry axis and with corresponding edges connected by lateral faces. For an equilateral ...

The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...

A run is a sequence of more than one consecutive identical outcomes, also known as a clump. Let R_p(r,n) be the probability that a run of r or more consecutive heads appears ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

The third singular value k_3, corresponding to K^'(k_3)=sqrt(3)K(k_3), (1) is given by k_3=sin(pi/(12))=1/4(sqrt(6)-sqrt(2)). (2) As shown by Legendre, ...

Gamma functions of argument 2z can be expressed in terms of gamma functions of smaller arguments. From the definition of the beta function, ...