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The log-likelihood function F(theta) is defined to be the natural logarithm of the likelihood function L(theta). More precisely, F(theta)=lnL(theta), and so in particular, ...

The Lommel polynomials R_(m,nu)(z) arise from the equation J_(m+nu)(z)=J_nu(z)R_(m,nu)(z)-J_(nu-1)(z)R_(m-1,nu+1)(z), (1) where J_nu(z) is a Bessel function of the first kind ...

The term "loop" has a number of meanings in mathematics. Most simply, a loop is a closed curve whose initial and final points coincide in a fixed point p known as the ...

A Lucas polynomial sequence is a pair of generalized polynomials which generalize the Lucas sequence to polynomials is given by W_n^k(x) = ...

The inconic having inconic parameters x:y:z=a/(b+c-a):b/(a+c-b):c/(a+b-c). Its center is the mittenpunkt M of the triangle and its Brianchon point is the Nagel point Na. The ...

An n×m matrix A^- is a 1-inverse of an m×n matrix A for which AA^-A=A. (1) The Moore-Penrose matrix inverse is a particular type of 1-inverse. A matrix equation Ax=b (2) has ...

Let f(x) be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then there is at least one point c in (a,b) such that ...

For triangles in the plane, AD·BE·CF=BD·CE·AF. (1) For spherical triangles, sinAD·sinBE·sinCF=sinBD·sinCE·sinAF. (2) This can be generalized to n-gons P=[V_1,...,V_n], where ...

A bounded plane convex region symmetric about a lattice point and with area >4 must contain at least three lattice points in the interior. In n dimensions, the theorem can be ...

A class of automata similar to cellular automata but which have a single "active" cell instead of updating all cells in parallel. In a mobile automaton, the evolution rules ...