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An Appell sequence is a Sheffer sequence for (g(t),t). Roman (1984, pp. 86-106) summarizes properties of Appell sequences and gives a number of specific examples. The ...

A homographic transformation x_1 = (ax+by+c)/(a^('')x+b^('')y+c^('')) (1) y_1 = (a^'x+b^'y+c^')/(a^('')x+b^('')y+c^('')) (2) with t_1 substituted for t according to ...

A surface of revolution defined by Kepler. It consists of more than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of ...

If A is a normed algebra, a net {e_i} in A is called an approximate identity for A if sup_(i)|e_i|<infty and if for each a in A, e_ia->a and ae_i->a. Though this definition ...

An approximate unit for a C^*-algebra A is an increasing net {u_lambda}_(lambda in Lambda) of positive elements in the closed unit ball of A such that a=lim_(lambda)au_lambda ...

An initial point that provides safe convergence of Newton's method (Smale 1981; Petković et al. 1997, p. 1).

If two quantities A and B are approximately equal, this is written A approx B.

The approximation problem is a well known problem of functional analysis (Grothendieck 1955). It asks to determine whether every compact operator T from a Banach space X to a ...

A Banach space X has the approximation property (AP) if, for every epsilon>0 and each compact subset K of X, there is a finite rank operator T in X such that for each x in K, ...

The mathematical study of how given quantities can be approximated by other (usually simpler) ones under appropriate conditions. Approximation theory also studies the size ...