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(d^2V)/(dv^2)+[a-2qcos(2v)]V=0 (1) (Abramowitz and Stegun 1972; Zwillinger 1997, p. 125), having solution y=C_1C(a,q,v)+C_2S(a,q,v), (2) where C(a,q,v) and S(a,q,v) are ...

A prime factorization algorithm also known as Pollard Monte Carlo factorization method. There are two aspects to the Pollard rho factorization method. The first is the idea ...

Calculus I

A path in the complex plane over which contour integration is performed to compute a contour integral. When choosing a contour to evaluate an integral on the real line, a ...

The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional integral as ...

An integral transform which is often written as an ordinary Laplace transform involving the delta function. The Laplace transform and Dirichlet series are special cases of ...

The Fredholm integral equation of the second kind f(x)=1+1/piint_(-1)^1(f(t))/((x-t)^2+1)dt that arises in electrostatics (Love 1949, Fox and Goodwin 1953, and Abbott 2002).

Suppose that in some neighborhood of x=0, F(x)=sum_(k=0)^infty(phi(k)(-x)^k)/(k!) (1) for some function (say analytic or integrable) phi(k). Then ...

A shortened term for integral transform. Geometrically, if S and T are two transformations, then the similarity transformation TST^(-1) is sometimes called the transform ...

Relates evolutes to single paths in the calculus of variations. Proved in the general case by Darboux and Zermelo in 1894 and Kneser in 1898. It states: "When a single ...