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The asymptotic form of the n-step Bernoulli distribution with parameters p and q=1-p is given by P_n(k) = (n; k)p^kq^(n-k) (1) ∼ 1/(sqrt(2pinpq))e^(-(k-np)^2/(2npq)) (2) ...

The generalized hypergeometric function is given by a hypergeometric series, i.e., a series for which the ratio of successive terms can be written ...

The Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques. To integrate a function f(x) over some interval [a,b], ...

A quadratic equation is a second-order polynomial equation in a single variable x ax^2+bx+c=0, (1) with a!=0. Because it is a second-order polynomial equation, the ...

A random number is a number chosen as if by chance from some specified distribution such that selection of a large set of these numbers reproduces the underlying ...

The (unilateral) Z-transform of a sequence {a_k}_(k=0)^infty is defined as Z[{a_k}_(k=0)^infty](z)=sum_(k=0)^infty(a_k)/(z^k). (1) This definition is implemented in the ...

The (unilateral) Z-transform of a sequence {a_k}_(k=0)^infty is defined as Z[{a_k}_(k=0)^infty](z)=sum_(k=0)^infty(a_k)/(z^k). (1) This definition is implemented in the ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...

A special case of the quadratic Diophantine equation having the form x^2-Dy^2=1, (1) where D>0 is a nonsquare natural number (Dickson 2005). The equation x^2-Dy^2=+/-4 (2) ...

In August 2002, M. Agrawal and colleagues announced a deterministic algorithm for determining if a number is prime that runs in polynomial time (Agrawal et al. 2004). While ...