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A formal power series is a special kind of formal series, of the form. where the called coefficients, are numbers or, more generally, elements of some ring, and the are formal powers of the symbol that is called an indeterminate or, commonly, a variable. Hence, power series can be viewed as a generalization of polynomials where the number of ...
Description. Perturbation theory develops an expression for the desired solution in terms of a formal power series known as a perturbation series in some "small" parameter, that quantifies the deviation from the exactly solvable problem. The leading term in this power series is the solution of the exactly solvable problem, while further terms ...
Power series. In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the n th term and c is a constant called the center of the series. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions.
In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by S. Bochner ( 1946 ). The term formal group sometimes means the same as formal group law, and sometimes means one of several generalizations.
Indeterminate (variable) In mathematics, an indeterminate or formal variable is a variable (a symbol, usually a letter) that is used purely formally in a mathematical expression, but does not stand for any value. [1][2][better source needed] In analysis, a mathematical expression such as is usually taken to represent a quantity whose ...
Generating function. In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series. There are various types of generating ...
A Riordan array is an infinite lower triangular matrix, , constructed from two formal power series, of order 0 and of order 1, such that . A Riordan array is an element of the Riordan group. [1] It was defined by mathematician Louis W. Shapiro and named after John Riordan. [1]
In a notable study of power conducted by social psychologists John R. P. French and Bertram Raven in 1959, power is divided into five separate and distinct forms. [1][2] They identified those five bases of power as coercive, reward, legitimate, referent, and expert. This was followed by Raven's subsequent addition in 1965 of a sixth separate ...