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Polynomials s_k(x) which form the Sheffer sequence for f(t)=-(2t)/(1-t^2) (1) and have exponential generating function ...

The Delta-variation is a variation in which the varied path over which an integral is evaluated may end at different times than the correct path, and there may be variation ...

In the calculus of variations, the condition f_(y^')(x,y,y^'(x_-))=f_(y^')(x,y,y^'(x_+)) must hold at a corner (x,y) of a minimizing arc E_(12).

An entire function which is a generalization of the Bessel function of the first kind defined by J_nu(z)=1/piint_0^picos(nutheta-zsintheta)dtheta. Anger's original function ...

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

The integral int_0^1x^p(1-x)^qdx, called the Eulerian integral of the first kind by Legendre and Whittaker and Watson (1990). The solution is the beta function B(p+1,q+1).

The finite zeros of the derivative r^'(z) of a nonconstant rational function r(z) that are not multiple zeros of r(z) are the positions of equilibrium in the field of force ...

If g(x) is differentiable at the point x and f(x) is differentiable at the point g(x), then f degreesg is differentiable at x. Furthermore, let y=f(g(x)) and u=g(x), then ...

A double integral is a two-fold multiple integral. Examples of definite double integrals evaluating to simple constants include int_0^1int_0^1(dxdy)/(1-x^2y^2) = 1/8pi^2 (1) ...

The set of terms of first-order logic (also known as first-order predicate calculus) is defined by the following rules: 1. A variable is a term. 2. If f is an n-place ...