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Consecutive number sequences are sequences constructed by concatenating numbers of a given type. Many of these sequences were considered by Smarandache and so are sometimes ...

If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in ...

An initial value problem is a problem that has its conditions specified at some time t=t_0. Usually, the problem is an ordinary differential equation or a partial ...

Various forms of opening and closing bracket-like delimiters are used for a number of distinct notational purposes in mathematics. The most common variants of bracket ...

The Weyl tensor is the tensor C_(abcd) defined by R_(abcd)=C_(abcd)+2/(n-2)(g_(a[c)R_d]b-g_(b[c)R_(d]a)) -2/((n-1)(n-2))Rg_(a[c)g_(d]b), (1) where R_(abcd) is the Riemann ...

Special functions which arise as solutions to second order ordinary differential equations are commonly said to be "of the first kind" if they are nonsingular at the origin, ...

A determinant which arises in the solution of the second-order ordinary differential equation x^2(d^2psi)/(dx^2)+x(dpsi)/(dx)+(1/4h^2x^2+1/2h^2-b+(h^2)/(4x^2))psi=0. (1) ...

Consider a second-order differential operator L^~u(x)=p_0(d^2u)/(dx^2)+p_1(du)/(dx)+p_2u, (1) where u=u(x) and p_i=p_i(x) are real functions of x on the region of interest ...

A determinant used to determine in which coordinate systems the Helmholtz differential equation is separable (Morse and Feshbach 1953). A determinant S=|Phi_(mn)|=|Phi_(11) ...

The method of d'Alembert provides a solution to the one-dimensional wave equation (partial^2y)/(partialx^2)=1/(c^2)(partial^2y)/(partialt^2) (1) that models vibrations of a ...