Power Series expansion of an eigenvalue

[ExplosivePete]

1. ... Expand the Eigenvalue as a power series in epsilon, up to second order:
λ=[3+√(1+4 ε^2)]V0 / 2

Homework Equations

I am familiar with power series, but I don't know how to expand this as one.[/B]

The Attempt at a Solution

:[/B] I have played around with the idea of using known power series of functions such as e^x, yet I haven't found a way to make that useful.

 

[BvU]

Dunno is not good enough according to PF guidelines
But do I detect a term ##\sqrt{1+4\varepsilon^2}## in there ?

 

[ExplosivePete]

Dunno is not good enough according to PF guidelines
But do I detect a term ##\sqrt{1+4\varepsilon^2}## in there ?

Please review my post again. Hopefully it is both more legible and up to PF guidelines.

 

[BvU]

I still detect a term ##
\sqrt{1+4\varepsilon^2\;}## ! How would you develop that into a power series in ##\varepsilon##, up to second order ?

And the guidelines tell you 'Dunno' ('Don't know') isn't good enough...