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The Fourier transform of the generalized function 1/x is given by F_x(-PV1/(pix))(k) = -1/piPVint_(-infty)^infty(e^(-2piikx))/xdx (1) = ...

The functional derivative is a generalization of the usual derivative that arises in the calculus of variations. In a functional derivative, instead of differentiating a ...

An algebraic equation is algebraically solvable iff its group is solvable. In order that an irreducible equation of prime degree be solvable by radicals, it is necessary and ...

A formula for numerical solution of differential equations, (1) where k_1 = hf(x_n,y_n) (2) k_2 = hf(x_n+1/2h,y_n+1/2k_1) (3) k_3 = ...

A generalization of an ordinary two-dimensional surface embedded in three-dimensional space to an (n-1)-dimensional surface embedded in n-dimensional space. A hypersurface is ...

The pedal curve for an n-cusped hypocycloid x = a((n-1)cost+cos[(n-1)t])/n (1) y = a((n-1)sint-sin[(n-1)t])/n (2) with pedal point at the origin is the curve x_p = ...

A function which is not defined explicitly, but rather is defined in terms of an algebraic relationship (which can not, in general, be "solved" for the function in question). ...

A quadratic surface given by the equation x^2+2rz=0.

If f is a continuous function that satisfies the Lipschitz condition |f(x,t)-f(y,t)|<=L|x-y| (1) in a surrounding of (x_0,t_0) in Omega subset ...

The formula giving the roots of a quadratic equation ax^2+bx+c=0 (1) as x=(-b+/-sqrt(b^2-4ac))/(2a). (2) An alternate form is given by x=(2c)/(-b+/-sqrt(b^2-4ac)). (3)