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11 21 8 61 22 58 241 52 328 444 1201 114 1452 4400 3708 7201 240 5610 32120 58140 33984 5040 (1) The second-order Eulerian triangle (OEIS A008517) is the number triangle ...

If one solution (y_1) to a second-order ordinary differential equation y^('')+P(x)y^'+Q(x)y=0 (1) is known, the other (y_2) may be found using the so-called reduction of ...

Consider a second-order differential operator L^~u(x)=p_0(d^2u)/(dx^2)+p_1(du)/(dx)+p_2u, (1) where u=u(x) and p_i=p_i(x) are real functions of x on the region of interest ...

Let the number of random walks on a d-D hypercubic lattice starting at the origin which never land on the same lattice point twice in n steps be denoted c_d(n). The first few ...

The metric tensor g on a smooth manifold M=(M,g) is said to be semi-Riemannian if the index of g is nonzero. In nearly all literature, the term semi-Riemannian is used ...

A separable extension K of a field F is one in which every element's algebraic number minimal polynomial does not have multiple roots. In other words, the minimal polynomial ...

The shah function is defined by m(x) = sum_(n=-infty)^(infty)delta(x-n) (1) = sum_(n=-infty)^(infty)delta(x+n), (2) where delta(x) is the delta function, so m(x)=0 for x not ...

The hyperbolic sine integral, often called the "Shi function" for short, is defined by Shi(z)=int_0^z(sinht)/tdt. (1) The function is implemented in the Wolfram Language as ...

A surface given by the parametric equations x(u,v) = u (1) y(u,v) = v (2) z(u,v) = 1/3u^3-1/2v^2. (3) The coefficients of the coefficients of the first fundamental form are E ...

Let delta=z>=z_(observed). A value 0<=alpha<=1 such that P(delta)<=alpha is considered "significant" (i.e., is not simply due to chance) is known as an alpha value. The ...