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Question: Where is the second solution?

Question:Where is the second solution?

SandorSzabo 607 Maple
infinity integer
December 20 2008
0

Assume n is positive integer.

dsolve((1-x^2)*(diff(y(x), x, x))-2*x*(diff(y(x), x))+(n*(1+n)-n^2/(1-x^2))*y(x), y(x))

Maple says

y(x) = _C1*LegendreP(n, n, x)+_C2*LegendreQ(n, n, x)

However

 dsolve((1-x^2)*(diff(y(x), x, x))-2*x*(diff(y(x), x))+(n*(1+n)-n^2/(1-x^2))*y(x), y(x), 'formal_solution', 'coeffs' = 'mhypergeom')

Maple says

y(x) = _C1*(Sum((-1)^(2*_n1)*GAMMA(_n1-(1/2)*n)*x^(2*_n1)/GAMMA(_n1+1), _n1 = 0 .. infinity))/GAMMA(-(1/2)*n)

Where is the second solution? 

I tried other ode and Maple gives the other formal solution also.

How could I obtain by Maple the second solution?

Thanks,    Sandor
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