power series

noun

, Mathematics.

an infinite series in which the terms are coefficients times successive powers of a given variable, or times products of powers of two or more variables.

power series

a mathematical series whose terms contain ascending positive integral powers of a variable, such as a 0 + a 1 x + a 2 x ² +…

power series

A sum of successively higher integral powers of a variable or combination of variables, each multiplied by a constant coefficient.

First recorded in 1890–95

The power series represents a continuous function in its domain of convergence (the end-points may have to be excluded).

The theory of power series has been developed chiefly from the point of view of the theory of functions of complex variables.

A power series converges uniformly in any interval contained within its domain of convergence, the end-points being excluded.

Thus we may make the power-series commence with 1, if we make the index-series commence with 0.

April 19, 2024tortuous

[tawr-choo-uhs ]

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