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A Colbert number is any prime number with more than 1000000 decimal digits whose discovery contributes to the long-sought after proof that k=78557 is the smallest Sierpiński ...

_0F_1(;a;z)=lim_(q->infty)_1F_1(q;a;z/q). (1) It has a series expansion _0F_1(;a;z)=sum_(n=0)^infty(z^n)/((a)_nn!) (2) and satisfies z(d^2y)/(dz^2)+a(dy)/(dz)-y=0. (3) It is ...

A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal ...

Elliptic alpha functions relate the complete elliptic integrals of the first K(k_r) and second kinds E(k_r) at elliptic integral singular values k_r according to alpha(r) = ...

Elliptic rational functions R_n(xi,x) are a special class of rational functions that have nice properties for approximating other functions over the interval x in [-1,1]. In ...

The elongated pentagonal gyrobicupola is a convex equilateral solid that is Johnson solid J_(39). The unit elongated pentagonal gyrobicupola has volume ...

The forward difference is a finite difference defined by Deltaa_n=a_(n+1)-a_n. (1) Higher order differences are obtained by repeated operations of the forward difference ...

The Franel numbers are the numbers Fr_n=sum_(k=0)^n(n; k)^3, (1) where (n; k) is a binomial coefficient. The first few values for n=0, 1, ... are 1, 2, 10, 56, 346, ... (OEIS ...

The global clustering coefficient C of a graph G is the ratio of the number of closed trails of length 3 to the number of paths of length two in G. Let A be the adjacency ...

Let 1/p+1/q=1 (1) with p, q>1. Then Hölder's inequality for integrals states that int_a^b|f(x)g(x)|dx<=[int_a^b|f(x)|^pdx]^(1/p)[int_a^b|g(x)|^qdx]^(1/q), (2) with equality ...