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The Minkowski measure of a bounded, closed set is the same as its Lebesgue measure.

A partial derivative of second or greater order with respect to two or more different variables, for example f_(xy)=(partial^2f)/(partialxpartialy). If the mixed partial ...

The second-order ordinary differential equation y^('')+alpha(x)y^'+x^2y^n=0.

Given a elliptic modulus k in an elliptic integral, the modular angle alpha is defined by k=sinalpha. An elliptic integral is written I(phi|m) when the parameter m is used, ...

The important property of Fourier transforms that F_x[cos(2pik_0x)f(x)](k) can be expressed in terms of F[f(x)]=F(k) as follows, ...

The partial differential equation (Cole and Cook 1986, p. 34; Zwillinger 1997, p. 134).

A technically defined group characterizing a system of linear differential equations y_j^'=sum_(k=1)^na_(jk)(x)y_k for j=1, ..., n, where a_(jk) are complex analytic ...

Another word for monotonic.

Always decreasing; never remaining constant or increasing. Also called strictly decreasing.

The integral phi(t,u)=int(e^(piitx^2+2piiux))/(e^(2piix)-1)dx which is related to the Jacobi theta functions, mock theta functions, Riemann zeta function, and Siegel theta ...