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In April 1999, Ed Pegg conjectured on sci.math that there were only finitely many zerofree cubes, to which D. Hickerson responded with a counterexample. A few days later, Lew ...

The modified Lommel functions of the first and second kind give the solution to the Lommel differential equation with a minus sign in front of the linear term, i.e., ...

Stratton (1935), Chu and Stratton (1941), and Rhodes (1970) define the spheroidal functions as those solutions of the differential equation (1) that remain finite at the ...

A generalization of the hypergeometric function identity (1) to the generalized hypergeometric function _3F_2(a,b,c;d,e;x). Darling's products are (2) and (3) which reduce to ...

The conditional intensity lambda(t) associated to a temporal point process N is defined to be the expected infinitesimal rate at which events are expected to occur around ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

sum_(n=0)^(infty)(-1)^n[((2n-1)!!)/((2n)!!)]^3 = 1-(1/2)^3+((1·3)/(2·4))^3+... (1) = _3F_2(1/2,1/2,1/2; 1,1;-1) (2) = [_2F_1(1/4,1/4; 1;-1)]^2 (3) = ...

The Mills ratio is defined as m(x) = 1/(h(x)) (1) = (S(x))/(P(x)) (2) = (1-D(x))/(P(x)), (3) where h(x) is the hazard function, S(x) is the survival function, P(x) is the ...

where _5F_4(a,b,c,d,e;f,g,h,i;z) is a generalized hypergeometric function and Gamma(z) is the gamma function. Bailey (1935, pp. 25-26) called the Dougall-Ramanujan identity ...

Dawson's integral (Abramowitz and Stegun 1972, pp. 295 and 319), also sometimes called Dawson's function, is the entire function given by the integral F(x) = ...