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The improvement of the convergence properties of a series, also called convergence acceleration or accelerated convergence, such that a series reaches its limit to within ...

An integral of the form intf(z)dz, (1) i.e., without upper and lower limits, also called an antiderivative. The first fundamental theorem of calculus allows definite ...

Successive application of Archimedes' recurrence formula gives the Archimedes algorithm, which can be used to provide successive approximations to pi (pi). The algorithm is ...

There are two kinds of power sums commonly considered. The first is the sum of pth powers of a set of n variables x_k, S_p(x_1,...,x_n)=sum_(k=1)^nx_k^p, (1) and the second ...

Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...

The Bernoulli numbers B_n are a sequence of signed rational numbers that can be defined by the exponential generating function x/(e^x-1)=sum_(n=0)^infty(B_nx^n)/(n!). (1) ...

The term "continued fraction" is used to refer to a class of expressions of which generalized continued fraction of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))) ...

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) ...

The so-called explicit formula psi(x)=x-sum_(rho)(x^rho)/rho-ln(2pi)-1/2ln(1-x^(-2)) gives an explicit relation between prime numbers and Riemann zeta function zeros for x>1 ...

The values of -d for which imaginary quadratic fields Q(sqrt(-d)) are uniquely factorable into factors of the form a+bsqrt(-d). Here, a and b are half-integers, except for ...