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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.’
‘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.’
‘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.’
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.’
‘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.’