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The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

The Radon transform is an integral transform whose inverse is used to reconstruct images from medical CT scans. A technique for using Radon transforms to reconstruct a map of ...

Mann's theorem is a theorem widely circulated as the "alpha-beta conjecture" that was subsequently proven by Mann (1942). It states that if A and B are sets of integers each ...

The proposition that every proper ideal of a Boolean algebra can be extended to a maximal ideal. It is equivalent to the Boolean representation theorem, which can be proved ...

The Prosthaphaeresis formulas, also known as Simpson's formulas, are trigonometry formulas that convert a product of functions into a sum or difference. They are given by ...

Quinn et al. (2007) investigated a class of N coupled oscillators whose bifurcation phase offset had a conjectured asymptotic behavior of sinphi∼1-c_1/N, with an experimental ...

The quintuple product identity, also called the Watson quintuple product identity, states (1) It can also be written (2) or (3) The quintuple product identity can be written ...

The Riemann-Siegel integral formula is the following representation of the xi-function xi(s) found in Riemann's Nachlass by Bessel-Hagen in 1926 (Siegel 1932; Edwards 2001, ...

The validity of a logical argument refers to whether or not the conclusion follows logically from the premises, i.e., whether it is possible to deduce the conclusion from the ...

The game of billiards is played on a rectangular table (known as a billiard table) upon which balls are placed. One ball (the "cue ball") is then struck with the end of a ...