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Let suma_k and sumb_k be two series with positive terms and suppose lim_(k->infty)(a_k)/(b_k)=rho. If rho is finite and rho>0, then the two series both converge or diverge.

Let N be an odd integer, and assume there exists a Lucas sequence {U_n} with associated Sylvester cyclotomic numbers {Q_n} such that there is an n>sqrt(N) (with n and N ...

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 ...

Dini Derivative, Lower Left Dini Derivative, Upper Left Dini Derivative, Upper Right Dini Derivative

Let {a_n} be a series of positive terms with a_(n+1)<=a_n. Then sum_(n=1)^(infty)a_n converges iff sum_(k=0)^infty2^ka_(2^k) converges.

A very useful active feedback method for controlling things like temperature control systems, servo motors, and flow control valves.

A test to determine if a given series converges or diverges.

Let {u_n(x)} be a sequence of functions. If 1. u_n(x) can be written u_n(x)=a_nf_n(x), 2. suma_n is convergent, 3. f_n(x) is a monotonic decreasing sequence (i.e., ...

An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points, but are not local ...

A robust estimation based on a rank test.