# DifferenceRoot help

I have being calculate some Series Coefficient and the result was and DifferenceRoot equation but i do not how

(-1)^v 2^(1 + v) 3^(-1 - v) Binomial[n + λ, n] Gamma[
1 + v] DifferenceRoot[
Function[{\[FormalY], \[FormalN]}, {3 \[FormalN] (\[FormalN] -
λ) \[FormalY][\[FormalN]] + (-6 - 13 \[FormalN] -
10 \[FormalN]^2 + 2 \[FormalN] n + 6 λ +
9 \[FormalN] λ) \[FormalY][
1 + \[FormalN]] + (22 + 31 \[FormalN] + 12 \[FormalN]^2 -
4 n - 4 \[FormalN] n - 12 λ -
9 \[FormalN] λ) \[FormalY][
2 + \[FormalN]] + (2 + \[FormalN]) (-11 - 6 \[FormalN] +
2 n + 3 λ) \[FormalY][
3 + \[FormalN]] + (2 + \[FormalN]) (3 + \[FormalN])
\[FormalY][4 + \[FormalN]] == 0, \[FormalY][-1] == 0, \[FormalY][0] ==
0, \[FormalY][1] ==
Hypergeometric2F1[1, -n, 1 + λ, 2/3], \[FormalY][2] == (
3 Hypergeometric2F1[1, -n, 1 + λ, 2/3] +
3 λ Hypergeometric2F1[1, -n, 1 + λ, 2/3] -
2 n Hypergeometric2F1[2, 1 - n, 2 + λ, 2/3])/(3 + 3 λ)}]][1 + v]


It is possible extraction as normal equation to get the coefficient of the series I have the feeling that Mathematica make a great job but the result is it not easy use to application; thanks anyway.

• What is your question? – MarcoB Apr 28 '18 at 22:29
• how extraction the coefficient of the DifferenceRoot – capea Apr 28 '18 at 22:34
• Thanks anyway MarcoB for your help i have been reading the Mathematica help center about the DifferentRoot but it is not very clear for me – capea Apr 28 '18 at 22:43
• Your code returns an error: DifferenceRoot::icond: Initial conditions should be of the form y[a] == b0, y[a + 1] == b1, ... please fix this so that it can be run. – bill s Apr 29 '18 at 1:23
• Assign values to n and v: Table[expr, {n, 0, 3}, {v, 1, 3}] // FullSimplify – Bob Hanlon Apr 29 '18 at 2:55