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A root-finding algorithm which converges to a complex root from any starting position. To motivate the formula, consider an nth order polynomial and its derivatives, P_n(x) = ...

The product of primes p_n#=product_(k=1)^np_k, (1) with p_n the nth prime, is called the primorial function, by analogy with the factorial function. Its logarithm is closely ...

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 ...

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 ...

The regulator of a number field K is a positive number associated with K. The regulator of an imaginary quadratic field is 1 and that of a real quadratic, imaginary cubic, or ...

A discontinuity is point at which a mathematical object is discontinuous. The left figure above illustrates a discontinuity in a one-variable function while the right figure ...

The logarithmic derivative of a function f is defined as the derivative of the logarithm of a function. For example, the digamma function is defined as the logarithmic ...

Let p_n be the nth prime, then the primorial (which is the analog of the usual factorial for prime numbers) is defined by p_n#=product_(k=1)^np_k. (1) The values of p_n# for ...

The function z=f(x)=ln(x/(1-x)). (1) This function has an inflection point at x=1/2, where f^('')(x)=(2x-1)/(x^2(x-1)^2)=0. (2) Applying the logit transformation to values ...

Scan the decimal expansion of a constant (including any digits to the left of the decimal point) until all n-digit strings have been seen (including 0-padded strings). The ...