Question: Hypergeometric series and Legendre ODE

Hi all,

While trying to solve the Legendre ODE, my serie (obtain by Frobenius method) was transform by Maple by the following:


> y1x(p);

                             /[  1    1   1  ]  [1]   2\
                    hypergeom|[- - p, - + - p], [-], x |
                             \[  2    2   2  ]  [2]    /

where y1x is my serie and p is the degree of the ODE.  But at the screen, the output is:

So my questions are

1.  What the 2 and the 1 around the F means?

2.  Is it normal that this special function is the solution of the Legendre ODE?

(in fact, I test it for different p::posint and it worked)

3.  Can someone help me to have the ratio |a(k+1)/a(k)| so I can do the ratio test for the convergence of that serie.  In fact, any additionnals informations ,other than the helps pages, would be very welcome.

Thanks in advance







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