An 'old wolf' may lose his teeth and also his memory so that I remember only now a problem I analysed two years ago. The 'general solution' of the ODE...

$\displaystyle x^{2}\ y^{''} + x\ y^{'} + y = 0$ (1)

... is...

$\displaystyle y(x)= c_{1}\ \text{icos} (x) + c_{2}\ \text{isin} (x)$ (2)

... where icos(*) and isin(*) are what I called 'I-functions' and theis properties I briefly described in ...

http://digilander.libero.it/luposaba...-functions.pdf
In particular the Laurent expansion's coefficients of the I'functions around $\displaystyle s=0$ are computed...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$