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Series reversion is the computation of the coefficients of the inverse function given those of the forward function. For a function expressed in a series with no constant ...

Simpson's rule is a Newton-Cotes formula for approximating the integral of a function f using quadratic polynomials (i.e., parabolic arcs instead of the straight line ...

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 ...

An ellipse is a curve that is the locus of all points in the plane the sum of whose distances r_1 and r_2 from two fixed points F_1 and F_2 (the foci) separated by a distance ...

The number of real roots of an algebraic equation with real coefficients whose real roots are simple over an interval, the endpoints of which are not roots, is equal to the ...

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 ...