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Let F be the Maclaurin series of a meromorphic function f with a finite or infinite number of poles at points z_k, indexed so that 0<|z_1|<=|z_2|<=|z_3|<=..., then a pole ...

For what value of x is f(x)=x^(1/x) a maximum? The maximum occurs at x=e, where f^'(x)=x^(-2+1/x)(1-lnx)=0, (1) which is zero at x=e and gives a maximum of ...

The fast Fourier transform (FFT) is a discrete Fourier transform algorithm which reduces the number of computations needed for N points from 2N^2 to 2NlgN, where lg is the ...

The usual number of scalar operations (i.e., the total number of additions and multiplications) required to perform n×n matrix multiplication is M(n)=2n^3-n^2 (1) (i.e., n^3 ...

Synthetic division is a shortcut method for dividing two polynomials which can be used in place of the standard long division algorithm. This method reduces the dividend and ...

The function frac(x) giving the fractional (noninteger) part of a real number x. The symbol {x} is sometimes used instead of frac(x) (Graham et al. 1994, p. 70; Havil 2003, ...

The area moment of inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or ...

Arithmetic is the branch of mathematics dealing with integers or, more generally, numerical computation. Arithmetical operations include addition, congruence calculation, ...

The polynomials defined by B_(i,n)(t)=(n; i)t^i(1-t)^(n-i), (1) where (n; k) is a binomial coefficient. The Bernstein polynomials of degree n form a basis for the power ...

The sequence a(n) given by the exponents of the highest power of 2 dividing n, i.e., the number of trailing 0s in the binary representation of n. For n=1, 2, ..., the first ...