Message Boards Message Boards

1 Reply
1 Total Likes
View groups...
Share this post:

Recursive Formula Involving a Summation

Posted 9 years ago

Hello I am trying to figure out how to correctly input this formula to find any number of coefficients I would like but somewhere along the way I seem to run into trouble. Could anyone tell me where I am going wrong? I thought using the RSolve function would easily solve this for me but all it gives me back is what I put in.

enter image description here

This is the format I am using, but it won't give me anything meaningful output:

RSolve[{a[n] == (n!/(\[Lambda] - \[Lambda]^n))*
    Sum[(a[n - k]*\[Lambda]^(n - k)*(-1)^k)/(k!*(n - 2 k)!), {k, 1, 
      Floor[n/2]}], a[n] == 1}, a[n], n]

Note that a[1]=1.

POSTED BY: Brian Razin

Asking for a closed form solution may be too much. You can calculate values:

a[1] = 1;
a[n_] := a[n] = (n!/(\[Lambda] - \[Lambda]^n))*
    Sum[(a[n - k]*\[Lambda]^(n - k)*(-1)^k)/(k!*(n - 2 k)!), {k, 1, 
TableForm@Table[Simplify@{n, a[n]}, {n, 1, 10}]
POSTED BY: Gianluca Gorni
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
or Discard

Group Abstract Group Abstract