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Let the probabilities of various classes in a distribution be p_1, p_2, ..., p_k, with observed frequencies m_1, m_2, ..., m_k. The quantity ...

A complex number may be taken to the power of another complex number. In particular, complex exponentiation satisfies (a+bi)^(c+di)=(a^2+b^2)^((c+id)/2)e^(i(c+id)arg(a+ib)), ...

If A=(a_(ij)) is a diagonal matrix, then Q(v)=v^(T)Av=suma_(ii)v_i^2 (1) is a diagonal quadratic form, and Q(v,w)=v^(T)Aw is its associated diagonal symmetric bilinear form. ...

The diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(76). This solid is the diminished polyhedron obtained by diminishing a small ...

Let f(z) = z+a_1+a_2z^(-1)+a_3z^(-2)+... (1) = zsum_(n=0)^(infty)a_nz^(-n) (2) = zg(1/z) (3) be a Laurent polynomial with a_0=1. Then the Faber polynomial P_m(f) in f(z) of ...

Finch (2010) gives an overview of known results for random Gaussian triangles. Let the vertices of a triangle in n dimensions be normal (normal) variates. The probability ...

H_n^((2))(z)=J_n(z)-iY_n(z), (1) where J_n(z) is a Bessel function of the first kind and Y_n(z) is a Bessel function of the second kind. Hankel functions of the second kind ...

Let b_1=1 and b_2=2 and for n>=3, let b_n be the least integer >b_(n-1) which can be expressed as the sum of two or more consecutive terms. The resulting sequence is 1, 2, 3, ...

The partial differential equation 1/(c^2)(partial^2psi)/(partialt^2)=(partial^2psi)/(partialx^2)-mu^2psi (1) that arises in mathematical physics. The quasilinear Klein-Gordon ...

The Lommel differential equation is a generalization of the Bessel differential equation given by z^2y^('')+zy^'+(z^2-nu^2)y=kz^(mu+1), (1) or, in the most general form, by ...