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The Gegenbauer polynomials C_n^((lambda))(x) are solutions to the Gegenbauer differential equation for integer n. They are generalizations of the associated Legendre ...

The decimal expansion of the Glaisher-Kinkelin constant is given by A=1.28242712... (OEIS A074962). A was computed to 5×10^5 decimal digits by E. Weisstein (Dec. 3, 2015). ...

The Jacobi polynomials, also known as hypergeometric polynomials, occur in the study of rotation groups and in the solution to the equations of motion of the symmetric top. ...

The numerical value of ln10 is given by ln10=2.302585092994045684... (OEIS A002392). It was computed to 10^(11) decimal digits by S. Kondo on May 20, 2011 (Yee). The Earls ...

pi may be computed using a number of iterative algorithms. The best known such algorithms are the Archimedes algorithm, which was derived by Pfaff in 1800, and the ...

A leaf of an unrooted tree is a node of vertex degree 1. Note that for a rooted or planted tree, the root vertex is generally not considered a leaf node, whereas all other ...

A technique used by André (1887) to provide an elegant solution to the ballot problem (Hilton and Pederson 1991) and in study of Wiener processes (Doob 1953; Papoulis 1984, ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

(dy)/(dx)+p(x)y=q(x)y^n. (1) Let v=y^(1-n) for n!=1. Then (dv)/(dx)=(1-n)y^(-n)(dy)/(dx). (2) Rewriting (1) gives y^(-n)(dy)/(dx) = q(x)-p(x)y^(1-n) (3) = q(x)-vp(x). (4) ...

The Brocard inellipse is the inconic with parameters x:y:z=1/a:1/b:1/c, (1) giving the trilinear equation ...