Search Results for ""

If f(z) is analytic throughout the annular region between and on the concentric circles K_1 and K_2 centered at z=a and of radii r_1 and r_2<r_1 respectively, then there ...

The Lerch transcendent is generalization of the Hurwitz zeta function and polylogarithm function. Many sums of reciprocal powers can be expressed in terms of it. It is ...

The nth root of the denominator B_n of the nth convergent A_n/B_n of a number x tends to a constant lim_(n->infty)B_n^(1/n) = e^beta (1) = e^(pi^2/(12ln2)) (2) = 3.275823... ...

The function lambda(n)=(-1)^(Omega(n)), (1) where Omega(n) is the number of not necessarily distinct prime factors of n, with Omega(1)=0. The values of lambda(n) for n=1, 2, ...

The standard Lorentzian inner product on R^4 is given by -dx_0^2+dx_1^2+dx_2^2+dx_3^2, (1) i.e., for vectors v=(v_0,v_1,v_2,v_3) and w=(w_0,w_1,w_2,w_3), ...

The Lovász number theta(G) of a graph G, sometimes also called the theta function of G, was introduced by Lovász (1979) with the explicit goal of estimating the Shannon ...

The Meijer G-function is a very general function which reduces to simpler special functions in many common cases. The Meijer G-function is defined by (1) where Gamma(s) is ...

A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one ...

The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the ...

An NSW number (named after Newman, Shanks, and Williams) is an integer m that solves the Diophantine equation 2n^2=m^2+1. (1) In other words, the NSW numbers m index the ...