1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Infinite power series

  1. Aug 19, 2008 #1
    1. The problem statement, all variables and given/known data

    Show that if a function f(x) can be expressed as an infinite power series, then it has the form

    f(x) = f(x0) + [tex]\sum^{\infty}_{n = 1}[/tex][tex]\frac{f^{n}(x0)}{n!}[/tex][tex](x - x0)^{}[/tex]

    2. Relevant equations



    3. The attempt at a solution

    I know that for an infinite power series:

    = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) + [tex]\frac{f''(a)}{2!}[/tex][tex](x - a)^{2}[/tex]....

    which can be simplified into the above expression. But is there any groundwork that the question asks to get to this point here? Im thinking for 6 marsk i cant just right down the two lines...
     
  2. jcsd
  3. Aug 19, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    A power series has the form [itex]
    f(x)= \sum^{\infty}_{n = 0}
    a_n (x-a)^n[/itex]. You want to show [itex]f_n(a)/n!=a_n[/itex]. Differentiate the power series n times and put x=a.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Infinite power series
  1. Infinite series. (Replies: 4)

  2. Infinite series. (Replies: 1)

Loading...