- #1

- 195

- 1

[itex]

\[

a_0=1,

\]

\[

a_1=p_1(1)a_0,

\]

\begin{equation}\label{recurr}

\begin{array}{ccc}

a_{n}=p_1(n) a_{n-1}+p_2(n) a_{n-2}, && n\ge2.\\

\end{array}

\end{equation}

[/itex]

where

[itex]

\[

p_1(n)=\frac{\delta^2/\alpha\gamma}{(n+k)^2-\beta^2/\alpha^2}

\]

[/itex]

and

[itex]

\[

p_2(n)=-\frac{1}{(n+k)^2-\beta^2/\alpha^2},

\]

[/itex]

with

[itex]

\[

k=\pm\frac{\beta}{\alpha}

\]

[/itex]

I'm interested in the asymptotic behavior of the coefficients

[itex]

\[

a_n^{(1)}\sim ???

\]

[/itex]

and

[itex]

\[

a_n^{(2)}\sim ???

\]

[/itex]

when

[itex]

n\mapsto\infty

[/itex]

Any ideas?