Search Results for ""

The word "rank" refers to several related concepts in mathematics involving graphs, groups, matrices, quadratic forms, sequences, set theory, statistics, and tensors. In ...

A recursive sequence {f(n)}_n, also known as a recurrence sequence, is a sequence of numbers f(n) indexed by an integer n and generated by solving a recurrence equation. The ...

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...

A method of determining coefficients alpha_k in a power series solution y(x)=y_0(x)+sum_(k=1)^nalpha_ky_k(x) of the ordinary differential equation L^~[y(x)]=0 so that ...

A pair of linear operators L and A associated with a given partial differential equation which can be used to solve the equation. However, it turns out to be very difficult ...

The differential equation describing exponential growth is (dN)/(dt)=rN. (1) This can be integrated directly int_(N_0)^N(dN)/N=int_0^trdt (2) to give ln(N/(N_0))=rt, (3) ...

A transformation of a polynomial equation f(x)=0 which is of the form y=g(x)/h(x) where g and h are polynomials and h(x) does not vanish at a root of f(x)=0. The cubic ...

For a second-order ordinary differential equation, y^('')+p(x)y^'+q(x)y=g(x). (1) Assume that linearly independent solutions y_1(x) and y_2(x) are known to the homogeneous ...

A quantity such as a polynomial discriminant which remains unchanged under a given class of algebraic transformations. Such invariants were originally called ...

Every irrational number x has an approximation constant c(x) defined by c(x)=lim inf_(q->infty)q|qx-p|, where p=nint(qx) is the nearest integer to qx and lim inf is the ...