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Let A=a_(ij) be a matrix with positive coefficients so that a_(ij)>0 for all i,j=1, 2, ..., n, then A has a positive eigenvalue lambda_0, and all its eigenvalues lie on the ...

Let C_(L,M) be a Padé approximant. Then C_((L+1)/M)S_((L-1)/M)-C_(L/(M+1))S_(L/(M+1)) = C_(L/M)S_(L/M) (1) C_(L/(M+1))S_((L+1)/M)-C_((L+1)/M)S_(L/(M+1)) = ...

If f^'(x) is continuous and the integral converges, int_0^infty(f(ax)-f(bx))/xdx=[f(0)-f(infty)]ln(b/a).

A frustum (unfortunately commonly misspelled "frustrum") is that portion of a solid which lies between two parallel planes cutting the solid. Degenerate cases are obtained ...

A system of linear differential equations (dy)/(dz)=A(z)y, (1) with A(z) an analytic n×n matrix, for which the matrix A(z) is analytic in C^_\{a_1,...,a_N} and has a pole of ...

Let the opposite sides of a convex cyclic hexagon be a, a^', b, b^', c, and c^', and let the polygon diagonals e, f, and g be so chosen that a, a^', and e have no common ...

A full angle, also called a complete angle, round angle, or perigon, is an angle equal to 2pi radians =360 degrees corresponding to the central angle of an entire circle. ...

By analogy with the geometric centroid, the centroid of an arbitrary function f(x) is defined as <x>=(intxf(x)dx)/(intf(x)dx), (1) where the integrals are taken over the ...

The convex hull of two or more functions is the largest function that is concave from above and does not exceed the given functions.

A function element is an ordered pair (f,U) where U is a disk D(Z_0,r) and f is an analytic function defined on U. If W is an open set, then a function element in W is a pair ...