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In mathematics, a polylogarithmic function in n is a polynomial in the logarithm of n, [1] () + () + + () +.The notation log k n is often used as a shorthand for (log n) k, analogous to sin 2 θ for (sin θ) 2.
In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs.
The geometric mean is more appropriate than the arithmetic mean for describing proportional growth, both exponential growth (constant proportional growth) and varying growth; in business the geometric mean of growth rates is known as the compound annual growth rate (CAGR). The geometric mean of growth over periods yields the equivalent constant ...
A log amplifier, also known as logarithmic amplifier or logarithm amplifier or log amp, is an amplifier for which the output voltage V out is K times the natural log of the input voltage V in. This can be expressed as,
The iterated logarithm is closely related to the generalized logarithm function used in symmetric level-index arithmetic.The additive persistence of a number, the number of times someone must replace the number by the sum of its digits before reaching its digital root, is ().
Of great interest in number theory is the growth rate of the prime-counting function. [3] [4] It was conjectured in the end of the 18th century by Gauss and by Legendre to be approximately where log is the natural logarithm, in the sense that / =
In computer science, binary search, also known as half-interval search, [1] logarithmic search, [2] or binary chop, [3] is a search algorithm that finds the position of a target value within a sorted array. [4] [5] Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target ...
Logarithmic convexity and Jensen's inequality together imply, for any positive real numbers , ... This growth is faster than exponential, ...