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The Risch algorithm is a decision procedure for indefinite integration that determines whether a given integral is elementary, and if so, returns a closed-form result for the ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

A second-order linear Hermitian operator is an operator L^~ that satisfies int_a^bv^_L^~udx=int_a^buL^~v^_dx. (1) where z^_ denotes a complex conjugate. As shown in ...

The Wiener-Hopf method is a powerful technique which enables certain linear partial differential equations subject to boundary conditions on semi-infinite domains to be ...

If an n-sided Poncelet transverse constructed for two given conic sections is closed for one point of origin, it is closed for any position of the point of origin. ...

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

As Lagrange showed, any irrational number alpha has an infinity of rational approximations p/q which satisfy |alpha-p/q|<1/(sqrt(5)q^2). (1) Furthermore, if there are no ...

An identity is a mathematical relationship equating one quantity to another (which may initially appear to be different).

The process of computing or obtaining an integral. A more archaic term for integration is quadrature.

If alpha is any number and m and n are integers, then there is a rational number m/n for which |alpha-m/n|<=1/n. (1) If alpha is irrational and k is any whole number, there ...