Power series, x=0

  • #1

Main Question or Discussion Point

what does it mean if y(x)=[itex]\sum[/itex][itex]^{∞}_{n=0}[/itex] an(x-x0)n
and y(0)=1 ?
does this mean that x0=0 and a0=1 ?
 

Answers and Replies

  • #2
lurflurf
Homework Helper
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It means y(0)=1.

That x0=0 and a0=1

is one (obvious) possibility, but sometimes other choices are used.

For example we might chose a different x0 is there is a singularity near zero and we need the series to converge is a certain range. Like if there were a singularity at x=-1 and we would like a series valid on (-1,3) we might choose x0=2. Then y(0)=1 means

1=y(0)=[itex]\sum[/itex][itex]^{∞}_{n=0}[/itex] an(-2)n

A bit tricky to work with, but not too bad.
 
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