In this instance the algebra of formal power series is the entire algebra from the monoid of pure quantities in excess of the underlying term ring.[fifteen] In the event the underlying term ring is really a differential algebra, then the algebra of official ability series is usually a differential algebra, with differentiation done term-by-phrase. Laurent series[edit]
and Enable the sequence of partial sums be provided by . When the sequence of partial sums converges to a definite value, the series is said to converge.
is any actual range, that one particular can find a reordering so the reordered series converges with sum equal to S displaystyle S
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