The coefficients of a certain power series

satisfy

and it is known that . Find .

Is this how it should be approached?

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- Jan 11th 2011, 01:50 PMdwsmithDE Power Series
The coefficients of a certain power series

satisfy

and it is known that . Find .

Is this how it should be approached? - Jan 11th 2011, 02:27 PMsnowtea
Try

- Jan 11th 2011, 02:28 PMdwsmith
- Jan 11th 2011, 02:30 PMsnowtea
Same as your previous question:

- Jan 11th 2011, 02:31 PMdwsmith
- Jan 11th 2011, 02:34 PMsnowtea
Well, it is the correct approach for this problem.

If you do not know the form it is better to take your recurrence:

Multiply every term by , and do the double summation of the entire expression, then simplify.

It becomes the form of the summation you are asking about. - Jan 11th 2011, 02:36 PMdwsmith
Now, my trouble is how do I use the initial condition?

- Jan 11th 2011, 02:38 PMsnowtea
You do realize that the summation you wrote gives you the DE:

Solve it like any other DE. - Jan 11th 2011, 02:38 PMdwsmith
Yes.

- Jan 11th 2011, 02:40 PMdwsmith
I can just solve that like any other PDE than?

- Jan 11th 2011, 02:41 PMsnowtea
So do you already have the general form of the solutions for the DE?

If so, just plug-in P(t,t) to solve with initial conditions right? Perhaps I'm missing something? - Jan 11th 2011, 02:42 PMdwsmith
- Jan 11th 2011, 06:07 PMdwsmith
I am struggling to obtain the book solution.

I tried B = 0 and D = 1/3; and D = 0 and B = 3 but nothing is happening.

Never mind I forgot to divide out a 2.