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The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
Negative refraction. Negative refraction is the electromagnetic phenomenon where light rays become refracted at an interface that is opposite to their more commonly observed positive refractive properties. Negative refraction can be obtained by using a metamaterial which has been designed to achieve a negative value for (electric) permittivity ...
Charge quantization is the principle that the charge of any object is an integer multiple of the elementary charge. Thus, an object's charge can be exactly 0 e, or exactly 1 e, −1 e, 2 e, etc., but not 1 / 2 e, or −3.8 e, etc. (There may be exceptions to this statement, depending on how "object" is defined; see below.)
It is known that ζ(3) is irrational (Apéry's theorem) and that infinitely many of the numbers ζ(2n + 1) : n ∈ , are irrational. There are also results on the irrationality of values of the Riemann zeta function at the elements of certain subsets of the positive odd integers; for example, at least one of ζ (5), ζ (7), ζ (9), or ζ (11 ...
Partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions ...
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator ( b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
As of September 2015, the largest confirmed Lucas prime is L 148091, which has 30950 decimal digits. [4] As of August 2022, the largest known Lucas probable prime is L 5466311, with 1,142,392 decimal digits. [5] If L n is prime then n is 0, prime, or a power of 2. [6] L 2 m is prime for m = 1, 2, 3, and 4 and no other known values of m.
Partial charge. In atomic physics, a partial charge (or net atomic charge) is a non- integer charge value when measured in elementary charge units. It is represented by the Greek lowercase delta (𝛿), namely 𝛿− or 𝛿+. Partial charges are created due to the asymmetric distribution of electrons in chemical bonds.