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the Pi function, i.e. the Gamma function when offset to coincide with the factorial; the complete elliptic integral of the third kind; the fundamental groupoid; osmotic pressure; represents: Archimedes' constant (more commonly just called Pi), the ratio of a circle's circumference to its diameter; the prime-counting function
Its value is +1 if n is the product of an even number of prime numbers, and −1 if it is the product of an odd number of primes. Explicitly, the fundamental theorem of arithmetic states that any positive integer n can be represented uniquely as a product of powers of primes: n = p 1 a 1 ⋯ p k a k , where p 1 < p 2 < ... < p k are primes and ...
In the field of representation theory in mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to the projective linear group = /, where GL(V) is the general linear group of invertible linear transformations of V over F, and F ∗ is the normal subgroup consisting of nonzero scalar multiples of the identity transformation (see ...
[6] [7] That D is strictly less than 2 follows from the conditions on and from above. Only after more than 30 years was this proved rigorously. [8] The term Weierstrass function is often used in real analysis to refer to any function with similar properties and construction to Weierstrass's original example.
In mathematics, the silver ratio is a geometrical proportion close to 70/29.Its exact value is 1 + √2, the positive solution of the equation x 2 = 2x + 1.. The name silver ratio results from analogy with the golden ratio, the positive solution of the equation x 2 = x + 1.
In physics, and especially scattering theory, the momentum-transfer cross section (sometimes known as the momentum-transport cross section [1]) is an effective scattering cross section useful for describing the average momentum transferred from a particle when it collides with a target.
There is a blue sapphire at the top of the diamond and a white sapphire at the bottom. [6] The rest of the border is outlined in ten pearls. [6] The fraternity also has a pledge pin that is a diamond with black enamel on the top half and gold enamel on the bottom half. [6] The fraternity's colors are black and gold. [6] Its flower is the ...