1. Nov 16, 2011 #1

   kahwawashay1

   

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

    

   kahwawashay1, Nov 16, 2011
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3. Nov 16, 2011 #2

   lurflurf

   

   Homework Helper

   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] a_n(-2)ⁿ
   
   A bit tricky to work with, but not too bad.

    

   lurflurf, Nov 16, 2011

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