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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. ...

A stellation is said to be fully supported if all its included cells are supported, i.e., if all its bottom faces are covered by their adjacent cells. In other words, every ...

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.

f(I) is the collection of all real-valued continuous functions defined on some interval I. f^((n))(I) is the collection of all functions in f(I) with continuous nth ...