Definition of power series in English:

power series


  • 1An infinite series of the form Σanxn (where n is a positive integer)

    • ‘The aim of these notes was to construct the analytical continuation of a power series outside its circle of convergence.’
    • ‘Not surprisingly, he also discovered the infinite power series for the cosine and the tangent.’
    • ‘The transformation of his conception of an analytic function from a differentiable function to a function expandable into a convergent power series was made during this early period of Weierstrass's mathematical activity.’
    • ‘This is called a power series for sin because it is a series in terms of powers of x.’
    • ‘Already at this stage he began to undertake research, investigating the problem of finding an estimate for the determinant generated by coefficients of a power series.’
    1. 1.1A generalization of a power series for more than one variable.
      • ‘These generating functions are infinite power series, and Euler was a master in manipulating them.’
      • ‘Or we may prescribe a seemingly much more powerful condition, namely, that the function possesses a development into power series about each point of the domain of definition.’
      • ‘It also contains continued fractions, quadratic equations, sums of power series and a table of sines.’
      • ‘He worked on power series and on potential theory.’
      • ‘Some of his most well-known contributions are a theorem connected to the Phragmén-Lindelöf principle, a theorem about the zeros of the V-function and several theorems about power series with integer coefficients.’