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Following Ramanujan (1913-1914), write product_(k=1,3,5,...)^infty(1+e^(-kpisqrt(n)))=2^(1/4)e^(-pisqrt(n)/24)G_n (1) ...

In statistics, sampling is the selection and implementation of statistical observations in order to estimate properties of an underlying population. Sampling is a vital part ...

Sigma is the eighteenth letter of the ancient Greek alphabet. As an upper case letter (Sigma), it is used as a symbol for sums and series. As a lower case letter (sigma) it ...

Define the minimal bounding rectangle as the smallest rectangle containing a given lattice polygon. If the perimeter of the lattice polygon is equal to that of its minimal ...

Analytic representations the symmetric triangle wave with period 2 and varying between -1 and 1 include f(x) = 2/pisin^(-1)[sin(pix)] (1) = 1-2|1-[2(1/2x+1/4 (mod 1))]| (2) = ...

Calculus II

There are essentially three types of Fisher-Tippett extreme value distributions. The most common is the type I distribution, which are sometimes referred to as Gumbel types ...

The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. For a sample size N, the mean ...

The plastic constant P, sometimes also called le nombre radiant, the minimal Pisot number, plastic number, plastic ratio, platin number, Siegel's number, or silver number, is ...

The power tower of order k is defined as a^^k=a^(a^(·^(·^(·^a))))_()_(k), (1) where ^ is Knuth up-arrow notation (Knuth 1976), which in turn is defined by ...