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Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...

Informally, self-similar objects with parameters N and s are described by a power law such as N=s^d, where d=(lnN)/(lns) is the "dimension" of the scaling law, known as the ...

An object is said to be self-similar if it looks "roughly" the same on any scale. Fractals are a particularly interesting class of self-similar objects. Self-similar objects ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_7=f(x_7). Then Hardy's rule approximating the ...

Wallis's constant is the real solution (x^3-2x-5)_1=2.0945514815... (OEIS A007493) to the cubic equation x^3-2x-5=0. It was solved by Wallis to illustrate Newton's method for ...

A general concept in category theory involving the globalization of topological or differential structures. The term derives from the Greek omicronlambdaomicronsigma (holos) ...

An "overdot" is a raised dot appearing above a symbol most commonly used in mathematics to indicate a derivative taken with respect to time (e.g., x^.=dx/dt). The expression ...

A root-finding algorithm also known as the tangent hyperbolas method or Halley's rational formula. As in Halley's irrational formula, take the second-order Taylor series ...

The differential equation describing exponential growth is (dN)/(dt)=rN. (1) This can be integrated directly int_(N_0)^N(dN)/N=int_0^trdt (2) to give ln(N/(N_0))=rt, (3) ...

The Mercator series, also called the Newton-Mercator series (Havil 2003, p. 33), is the Taylor series for the natural logarithm ln(1+x) = sum_(k=1)^(infty)((-1)^(k+1))/kx^k ...