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The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives. An ODE of order n is an ...

A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ..., n^2 arranged such that the sum of the n numbers in any horizontal, ...

A generalized continued fraction is an expression of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))), (1) where the partial numerators a_1,a_2,... and partial ...

As a part of the study of Waring's problem, it is known that every positive integer is a sum of no more than 9 positive cubes (g(3)=9), that every "sufficiently large" ...

The term "characteristic" has many different uses in mathematics. In general, it refers to some property that inherently describes a given mathematical object, for example ...

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) ...

The inverse erf function is the inverse function erf^(-1)(z) of the erf function erf(x) such that erf(erf^(-1)(x)) = x (1) erf^(-1)(erf(x)) = x, (2) with the first identity ...

A root-finding algorithm which makes use of a third-order Taylor series f(x)=f(x_n)+f^'(x_n)(x-x_n)+1/2f^('')(x_n)(x-x_n)^2+.... (1) A root of f(x) satisfies f(x)=0, so 0 ...

The Gauss-Kuzmin distribution is the distribution of occurrences of a positive integer k in the continued fraction of a random (or "generic") real number. Consider xi_n ...