Search Results for ""

f_p=f_0+1/2p(p+1)delta_(1/2)-1/2(p-1)pdelta_(-1/2) +(S_3+S_4)delta_(1/2)^3+(S_3-S_4)delta_(-1/2)^3+..., (1) for p in [-1/2,1/2], where delta is the central difference and ...

Let R[z]>0, 0<=alpha,beta<=1, and Lambda(alpha,beta,z)=sum_(r=0)^infty[lambda((r+alpha)z-ibeta)+lambda((r+1-alpha)z+ibeta)], (1) where lambda(x) = -ln(1-e^(-2pix)) (2) = ...

Let J_nu(z) be a Bessel function of the first kind, Y_nu(z) a Bessel function of the second kind, and K_nu(z) a modified Bessel function of the first kind. Also let R[z]>0 ...

The geometric mean is smaller than the arithmetic mean, (product_(i=1)^Nn_i)^(1/N)<=(sum_(i=1)^(N)n_i)/N, with equality in the cases (1) N=1 or (2) n_i=n_j for all i,j.

If g is continuous and mu,nu>0, then int_0^t(t-xi)^(mu-1)dxiint_0^xi(xi-x)^(nu-1)g(xi,x)dx =int_0^tdxint_x^t(t-xi)^(mu-1)(xi-x)^(nu-1)g(xi,x)dxi.

A^n+B^n=sum_(j=0)^(|_n/2_|)(-1)^jn/(n-j)(n-j; j)(AB)^j(A+B)^(n-2j), where |_x_| is the floor function and (n; k) is a binomial coefficient.

For a curve with first fundamental form ds^2=Edu^2+2Fdudv+Gdv^2, (1) the Gaussian curvature is K=(M_1-M_2)/((EG-F^2)^2), (2) where M_1 = |-1/2E_(vv)+F_(uv)-1/2G_(uu) 1/2E_u ...

Let {p_n(x)} be orthogonal polynomials associated with the distribution dalpha(x) on the interval [a,b]. Also let rho=c(x-x_1)(x-x_2)...(x-x_l) (for c!=0) be a polynomial of ...

For R[a+b-c-d]<-1 and a and b not integers,

The infinite product identity Gamma(1+v)=2^(2v)product_(m=1)^infty[pi^(-1/2)Gamma(1/2+2^(-m)v)], where Gamma(x) is the gamma function.