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1An infinite series of the form Σanxn (where n is a positive integer).
‘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.’
‘Not surprisingly, he also discovered the infinite power series for the cosine and the tangent.’
‘The aim of these notes was to construct the analytical continuation of a power series outside its circle of convergence.’
‘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.’
1.1A generalization of a power series for more than one variable.
‘He worked on power series and on potential theory.’
‘It also contains continued fractions, quadratic equations, sums of power series and a table of sines.’
‘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.’
‘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.’
‘These generating functions are infinite power series, and Euler was a master in manipulating them.’