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The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved in 1737.. Like rational numbers, the reciprocals of primes have repeating decimal representations.
The sum of the reciprocals of the powerful numbers is close to 1.9436 . [4] The reciprocals of the factorials sum to the transcendental number e (one of two constants called "Euler's number"). The sum of the reciprocals of the square numbers (the Basel problem) is the transcendental number π 2 / 6 , or ζ(2) where ζ is the Riemann zeta ...
The reciprocal function: y = 1/x.For every x except 0, y represents its multiplicative inverse. The graph forms a rectangular hyperbola.. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x −1, is a number which when multiplied by x yields the multiplicative identity, 1.
The harmonic number with = ⌊ ⌋ (red line) with its asymptotic limit + (blue line) where is the Euler–Mascheroni constant.. In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers: [1] = + + + + = =.
If the original random variable X is uniformly distributed on the interval (a,b), where a>0, then the reciprocal variable Y = 1 / X has the reciprocal distribution which takes values in the range (b −1,a −1), and the probability density function in this range is =, and is zero elsewhere.
Reciprocal polynomial, a polynomial obtained from another polynomial by reversing its coefficients; Reciprocal rule, a technique in calculus for calculating derivatives of reciprocal functions; Reciprocal spiral, a plane curve; Reciprocal averaging, a statistical technique for aggregating categorical data
Reciprocal polynomials have several connections with their original polynomials, including: deg p = deg p ∗ if is not 0.; p(x) = x n p ∗ (x −1). [2]α is a root of a polynomial p if and only if α −1 is a root of p ∗.
The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of the numbers, that is, ... x and y, and a nomogram to calculate it. The blue line ...