Search Results for ""

Gives a matrix representation b_i of a braid group in terms of (n-1)×(n-1) matrices. A -t always appears in the (i,i) position. b_1 = [-t 0 0 ... 0; -1 1 0 ... 0; 0 0 1 ... ...

A Banach algebra A is called contractible if H^1(A,X)=Z^1(A,X)/B^1(A,X)=0 for all Banach A-bimodules X (Helemskii 1989, 1997). A C^*-algebra is contractible if and only if it ...

The truth of an infinite sequence of propositions P_i for i=1, ..., infty is established if (1) P_1 is true, and (2) P_k implies P_(k+1) for all k. This principle is ...

A sequence of polynomials p_i(x), for i=0, 1, 2, ..., where p_i(x) is exactly of degree i for all i.

Expanding the Riemann zeta function about z=1 gives zeta(z)=1/(z-1)+sum_(n=0)^infty((-1)^n)/(n!)gamma_n(z-1)^n (1) (Havil 2003, p. 118), where the constants ...

As defined by Erdélyi et al. (1981, p. 20), the G-function is given by G(z)=psi_0(1/2+1/2z)-psi_0(1/2z), (1) where psi_0(z) is the digamma function. Integral representations ...

The Fibonacci numbers are the sequence of numbers {F_n}_(n=1)^infty defined by the linear recurrence equation F_n=F_(n-1)+F_(n-2) (1) with F_1=F_2=1. As a result of the ...

The complementary Bell numbers, also called the Uppuluri-Carpenter numbers, B^~_n=sum_(k=0)^n(-1)^kS(n,k) (1) where S(n,k) is a Stirling number of the second kind, are ...

Odd values of Q(n) are 1, 1, 3, 5, 27, 89, 165, 585, ... (OEIS A051044), and occur with ever decreasing frequency as n becomes large (unlike P(n), for which the fraction of ...

The dihedral group D_4 is one of the two non-Abelian groups of the five groups total of group order 8. It is sometimes called the octic group. An example of D_4 is the ...