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{{r|Power series}}

===Power series=== The [[radius of convergence]] of a [[power series]] is the distance the nearest [[singularity (mathematics)|singularity]]. T

{{r|Power series}}

===Power series of a function===

===Power series=== ...[[René Descartes]]), became tractable via such infinite sums now called [[power series]].<ref name=Arnold/>

Most important are two classes of series of functions: [[power series|power]] (especially, [[Taylor series|Taylor]]) series whose terms are power

This energy can be expanded in a power series&mdash; the '''multipole expansion'''&mdash;in the inverse distance of ''A'

...'''Fibonacci generating function''' is defined as the sum of the following power series:

...] of [[disk (mathematics)|disk]]s, centered at that point) as a convergent power series in the variables. This condition is stronger than the [[Cauchy-Riemann equa

...heory|ring]] ''R''. Similarly we may define ''D'' on the ring of [[formal power series]] <math>R[[X]]</math>.

...llows one to view a polynomial ring as a [[subring]] of a [[ring of formal power series]]. This is the approach that will be used in this article.

...r]]s in 1897, looking for a way to bring the ideas and the techniques of [[power series]] within [[number theory]].

...math>z = i\theta</math> and comparing terms with the usual [[Taylor series|power series expansions]] of <math>\sin \theta</math> and <math>\cos \theta</math>.

...extension in areas such as [[probability theory]] and the calculation of [[power series]]. Many expressions involving products of successive integers can be writte

...math>z = i\theta</math> and comparing terms with the usual [[Taylor series|power series expansions]] of <math>\sin \theta</math> and <math>\cos \theta</math>.

...someone found a remarkable equality between the Pascal's triangle and a [[power series]] of square [[matrix|matrices]].<ref>For instance, see Gottfried Helms, [ht

[[Formal group law]]s are certain [[formal power series]] which have properties much like a group operation.

...st of his work is restricted is restricted to the formal manipulation of [[power series]]. He did, however, do some very notable (though not fully rigorous) early