Search Results for ""

Let P be a prime ideal in D_m not containing m. Then (Phi(P))=P^(sumtsigma_t^(-1)), where the sum is over all 1<=t<m which are relatively prime to m. Here D_m is the ring of ...

The ith Stiefel-Whitney class of a real vector bundle (or tangent bundle or a real manifold) is in the ith cohomology group of the base space involved. It is an obstruction ...

The Stiefel-Whitney number is defined in terms of the Stiefel-Whitney class of a manifold as follows. For any collection of Stiefel-Whitney classes such that their cup ...

The Stiefel manifold of orthonormal k-frames in R^n is the collection of vectors (v_1, ..., v_k) where v_i is in R^n for all i, and the k-tuple (v_1, ..., v_k) is ...

Orthogonal polynomials associated with weighting function w(x) = pi^(-1/2)kexp(-k^2ln^2x) (1) = pi^(-1/2)kx^(-k^2lnx) (2) for x in (0,infty) and k>0. Defining ...

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 ...

The Stieltjes integral is a generalization of the Riemann integral. Let f(x) and alpha(x) be real-valued bounded functions defined on a closed interval [a,b]. Take a ...

The m+1 ellipsoidal harmonics when kappa_1, kappa_2, and kappa_3 are given can be arranged in such a way that the rth function has r-1 zeros between -a^2 and -b^2 and the ...

The integral transform (Kf)(x)=Gamma(p)int_0^infty(x+t)^(-p)f(t)dt. Note the lower limit of 0, not -infty as implied in Samko et al. (1993, p. 23, eqn. 1.101).

The signed Stirling numbers of the first kind are variously denoted s(n,m) (Riordan 1980, Roman 1984), S_n^((m)) (Fort 1948, Abramowitz and Stegun 1972), S_n^m (Jordan 1950). ...