Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Questions about integration of power series

  1. Nov 9, 2008 #1
    Lets say we have this series:

    a0+ a1(x-k)^1 +a2(x-k)^2 +a3(x-k)^3 = s(x)

    If I integrate the series a theorem in the books says that I will get the antiderivate S(x)+C, but won't C allways be equal to zero?
     
  2. jcsd
  3. Nov 9, 2008 #2

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Why should it be zero? Upon taking the derivative of S(x) + C, one obtains the original sum s(x).

    C is arbitrary by definition, unless it is fixed by a boundary condition.
     
  4. Nov 9, 2008 #3
    I read this in another theorem:

    f(x)= (sigma from n=0 to eternity) an(x-b)^n an is like a0 a1 a2 a3 etc

    then:
    integrate from b to x f(t) dt= (sigma from n=0 to eternity) an/(n+1)* (x-b)^(n+1)


    Here it is no constant, how can I keep track of the constants?
     
  5. Nov 9, 2008 #4

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Note that in this case you are integrating between limits, i.e. you are evaluating the definite integral, whereas in the previous case you were evaluating the indefinite integral.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Questions about integration of power series
Loading...