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A universal differential equation (UDE) is a nontrivial differential-algebraic equation with the property that its solutions approximate to arbitrary accuracy any continuous ...

The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. In a ...

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

The generalized Riemann hypothesis conjectures that neither the Riemann zeta function nor any Dirichlet L-series has a zero with real part larger than 1/2. Compare with ...

e^(izcostheta)=sum_(n=-infty)^inftyi^nJ_n(z)e^(intheta), where J_n(z) is a Bessel function of the first kind. The identity can also be written ...

The Longuet-Higgins point is the radical center of the circles centered at the vertices A, B, and C of a reference triangle with respective radii b+c, c+a, and a+b. It has ...

The Lerch transcendent is generalization of the Hurwitz zeta function and polylogarithm function. Many sums of reciprocal powers can be expressed in terms of it. It is ...

An asymptotic series is a series expansion of a function in a variable x which may converge or diverge (Erdélyi 1987, p. 1), but whose partial sums can be made an arbitrarily ...

Brocard's conjecture states that pi(p_(n+1)^2)-pi(p_n^2)>=4 for n>=2, where pi(n) is the prime counting function and p_n is the nth prime. For n=1, 2, ..., the first few ...

The negative binomial distribution, also known as the Pascal distribution or Pólya distribution, gives the probability of r-1 successes and x failures in x+r-1 trials, and ...