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Consider the sequence of partial sums defined by s_n=sum_(k=1)^n(-1)^kk^(1/k). (1) As can be seen in the plot above, the sequence has two limit points at -0.812140... and ...

Measure theory is the study of measures. It generalizes the intuitive notions of length, area, and volume. The earliest and most important examples are Jordan measure and ...

The moment of inertia with respect to a given axis of a solid body with density rho(r) is defined by the volume integral I=intrho(r)r__|_^2dV, (1) where r__|_ is the ...

A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...

N. Nielsen (1909) and Ramanujan (Berndt 1985) considered the integrals a_k=int_1^2((lnx)^k)/(x-1)dx. (1) They found the values for k=1 and 2. The general constants for k>3 ...

Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll. The ...

Petersen's theorem states that every cubic graph with no bridges has a perfect matching (Petersen 1891; Frink 1926; König 1936; Skiena 1990, p. 244). In fact, this theorem ...

For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...

A prolate spheroid is a spheroid that is "pointy" instead of "squashed," i.e., one for which the polar radius c is greater than the equatorial radius a, so c>a (called ...

Quasi-Monte Carlo integration is a method of numerical integration that operates in the same way as Monte Carlo integration, but instead uses sequences of quasirandom numbers ...