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The square of the area of the base (i.e., the face opposite the right trihedron) of a trirectangular tetrahedron is equal to the sum of the squares of the areas of its other ...

The q-analog of the binomial theorem (1-z)^n=1-nz+(n(n-1))/(1·2)z^2-(n(n-1)(n-2))/(1·2·3)z^3+... (1) is given by (1-z/(q^n))(1-z/(q^(n-1)))...(1-z/q) ...

The q-digamma function psi_q(z), also denoted psi_q^((0))(z), is defined as psi_q(z)=1/(Gamma_q(z))(partialGamma_q(z))/(partialz), (1) where Gamma_q(z) is the q-gamma ...

Let sum_(k=0)^(infty)a_k=a and sum_(k=0)^(infty)c_k=c be convergent series such that lim_(k->infty)(a_k)/(c_k)=lambda!=0. Then ...

A product involving an infinite number of terms. Such products can converge. In fact, for positive a_n, the product product_(n=1)^(infty)a_n converges to a nonzero number iff ...

P(n), sometimes also denoted p(n) (Abramowitz and Stegun 1972, p. 825; Comtet 1974, p. 94; Hardy and Wright 1979, p. 273; Conway and Guy 1996, p. 94; Andrews 1998, p. 1), ...

A sequence of polynomials p_n satisfying the identities p_n(x+y)=sum_(k>=0)(n; k)p_k(x)p_(n-k)(y).

sum_(i=1)^n((partialu)/(partialx_i))^2=1.

Pre-Algebra

A number x in which the first n decimal digits of the fractional part frac(x) sum to 666 is known as an evil number (Pegg and Lomont 2004). However, the term "evil" is also ...