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The general nonhomogeneous differential equation is given by x^2(d^2y)/(dx^2)+alphax(dy)/(dx)+betay=S(x), (1) and the homogeneous equation is x^2y^('')+alphaxy^'+betay=0 (2) ...

The amazing polynomial identity communicated by Euler in a letter to Goldbach on April 12, 1749 (incorrectly given as April 15, 1705--before Euler was born--in Conway and Guy ...

The four parameters e_0, e_1, e_2, and e_3 describing a finite rotation about an arbitrary axis. The Euler parameters are defined by e_0 = cos(phi/2) (1) e = [e_1; e_2; e_3] ...

A differential of the form df=P(x,y)dx+Q(x,y)dy (1) is exact (also called a total differential) if intdf is path-independent. This will be true if ...

The expectation value of a function f(x) in a variable x is denoted <f(x)> or E{f(x)}. For a single discrete variable, it is defined by <f(x)>=sum_(x)f(x)P(x), (1) where P(x) ...

The exterior derivative of a function f is the one-form df=sum_(i)(partialf)/(partialx_i)dx_i (1) written in a coordinate chart (x_1,...,x_n). Thinking of a function as a ...

The extouch triangle DeltaT_1T_2T_3 is the triangle formed by the points of tangency of a triangle DeltaA_1A_2A_3 with its excircles J_1, J_2, and J_3. The points T_1, T_2, ...

A continuous statistical distribution which arises in the testing of whether two observed samples have the same variance. Let chi_m^2 and chi_n^2 be independent variates ...

The determination of a set of factors (divisors) of a given integer ("prime factorization"), polynomial ("polynomial factorization"), etc., which, when multiplied together, ...

If {f_n} is a sequence of nonnegative measurable functions, then intlim inf_(n->infty)f_ndmu<=lim inf_(n->infty)intf_ndmu. (1) An example of a sequence of functions for which ...