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Harmonic numbers are related to the harmonic mean in that the n-th harmonic number is also n times the reciprocal of the harmonic mean of the first n positive integers. Harmonic numbers have been studied since antiquity and are important in various branches of number theory .
In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means.. It is the most appropriate average for ratios and rates such as speeds, [1] [2] and is normally only used for positive arguments.
In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the fundamental frequency of a periodic signal. The fundamental frequency is also called the 1st harmonic ; the other harmonics are known as higher harmonics .
[1] [2] Every term of the harmonic series after the first is the harmonic mean of the neighboring terms, so the terms form a harmonic progression; the phrases harmonic mean and harmonic progression likewise derive from music. [2] Beyond music, harmonic sequences have also had a certain popularity with architects.
In number theory, the harmonic numbers are the sums of the inverses of integers, forming the harmonic series. Harmonic number may also refer to: Harmonic, a periodic wave with a frequency that is an integral multiple of the frequency of another wave; Harmonic divisor numbers, also called Ore numbers or Ore's harmonic numbers, positive integers ...
In mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are 1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190 (sequence A001599 in the OEIS).
Harmonic (NAS: HLIT) is expected to report Q4 earnings on Jan. 29. Here's what Wall Street wants to see: The 10-second takeaway Comparing the upcoming quarter to the prior-year quarter, average ...
Harmonic mean denoted by H, geometric by G, arithmetic by A and quadratic mean (also known as root mean square) denoted by Q. Comparison of the arithmetic, geometric and harmonic means of a pair of numbers. The vertical dashed lines are asymptotes for the harmonic means.