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Let F(nu) and G(nu) be the Fourier transforms of f(t) and g(t), respectively. Then int_(-infty)^inftyf(t)g^_(t)dt ...

The kth percentile P_k is that value of x, say x_k, which corresponds to a cumulative frequency of Nk/100, where N is the sample size.

All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.

A^*(x)=sum_(lambda_n<=x)^'a_n=1/(2pii)int_(c-iinfty)^(c+iinfty)f(s)(e^(sx))/sds, where f(s)=suma_ne^(-lambda_ns).

The first and second Pöschl-Teller differential equations are given by y^('')-{a^2[(kappa(kappa-1))/(sin^2(ax))+(lambda(lambda-1))/(cos^2(ax))]-b^2}y=0 and ...

The polyhedral formula generalized to a surface of genus g, V-E+F=chi(g) where V is the number of polyhedron vertices, E is the number of polyhedron edges, F is the number of ...

The point group C_1 is a group on a single element that is isomorphic to the trivial group. Its character table is given below. C_1 1 1 1

The breaking up of self-intersecting polygons into simple polygons (illustrated above) is also called tessellation (Woo et al. 1999).

One of the symmetry groups of the Platonic solids. There are three polyhedral groups: the tetrahedral group of order 12, the octahedral group of order 24, and the icosahedral ...

The system of partial differential equations u_t+uu_x+vu_y=U_t+UU_x+mu/rhou_(yy) u_x+v_y=0.