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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 ...

An expression which is a sentence or which contains variables and becomes a sentence upon appropriate substitutions for these variables (Carnap 1958, p. 24). Sentential ...

The Riemann-Siegel formula is a formula discovered (but not published) by Riemann for computing an asymptotic formula for the Riemann-Siegel function theta(t). The formula ...

The sine function sinx is one of the basic functions encountered in trigonometry (the others being the cosecant, cosine, cotangent, secant, and tangent). Let theta be an ...

The haversine, also called the haversed sine, is a little-used entire trigonometric function defined by hav(z) = 1/2vers(z) (1) = 1/2(1-cosz) (2) = sin^2(1/2z), (3) where ...

A class number formula is a finite series giving exactly the class number of a ring. For a ring of quadratic integers, the class number is denoted h(d), where d is the ...

Lehmer's formula is a formula for the prime counting function, pi(x) = (1) where |_x_| is the floor function, a = pi(x^(1/4)) (2) b = pi(x^(1/2)) (3) b_i = pi(sqrt(x/p_i)) ...

The Sherman-Morrison formula is a formula that allows a perturbed matrix to be computed for a change to a given matrix A. If the change can be written in the form u tensor v ...

Let phi(x_1,...,x_m) be an L_(exp) formula, where L_(exp)=L union {e^x} and L is the language of ordered rings L={+,-,·,<,0,1}. Then there exist n>=m and f_1,...,f_s in ...

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...