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Watson (1939) considered the following three triple integrals, I_1 = 1/(pi^3)int_0^piint_0^piint_0^pi(dudvdw)/(1-cosucosvcosw) (1) = (4[K(1/2sqrt(2))]^2)/(pi^2) (2) = ...

The Wigner 3j-symbols (j_1 j_2 j_3; m_1 m_2 m_3), also known as "3j symbols" (Messiah 1962, p. 1056) or Wigner coefficients (Shore and Menzel 1968, p. 275) are quantities ...

The Wigner 6j-symbols (Messiah 1962, p. 1062), commonly simply called the 6j-symbols, are a generalization of Clebsch-Gordan coefficients and Wigner 3j-symbol that arise in ...

Given a pick-7 lottery with 23 numbers that pays a prize to anyone matching at least 4 of the 7 numbers, there is a set of 253 tickets that guarantees a win. This set ...

A problem posed by the Slovak mathematician Stefan Znám in 1972 asking whether, for all integers k>=2, there exist k integers x_1,...,x_k all greater than 1 such that x_i is ...

Pre-Algebra

Pre-Calculus

The nth k-statistic k_n is the unique symmetric unbiased estimator of the cumulant kappa_n of a given statistical distribution, i.e., k_n is defined so that <k_n>=kappa_n, ...

The q-analog of the Pochhammer symbol defined by (a;q)_k={product_(j=0)^(k-1)(1-aq^j) if k>0; 1 if k=0; product_(j=1)^(|k|)(1-aq^(-j))^(-1) if k<0; ...

Apéry's constant is defined by zeta(3)=1.2020569..., (1) (OEIS A002117) where zeta(z) is the Riemann zeta function. Apéry (1979) proved that zeta(3) is irrational, although ...