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Question: Using Maple's sum fuction to generate Legendre polynomials

Question:Using Maple's sum fuction to generate Legendre polynomials

Jean-Guy Murray 16 Maple
December 22 2006
0
I have solve the Legendre equation (1-x^2)y''-2xy'+alpha(alpha+1)y=0. The solutions are: y1=1-alpha(alpha+1)x^2/2! +alpha(alpha-2)(alpha+1)(alpha+3)x^4/4! +sum{(-1)^m [(alpha-1)...(alpha-2m+2)][(alpha+2)...(alpha+2m-1)]x^2m/(2m)!} y2=x-(alpha-1)(alpha+2)x^3/3!+(alpha-1)(alpha-3)(alpha+2)(alpha+4)x^5/5!+sum{(-1)^m[(alpha-1)...(alpha-2m+1][(alpha+2)...(alpha+2m)]x^2m+1/(2m)!} I tried to obtain a Legendre polynomial, say P5(x), with Maple'sum function by plugging in the general expression but I do not obtain the correct answer. Can someone indicate how this can be done. Thank you kindly. jg
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