ahmadtalaei

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Anyone can help me to convert the following maple solution expressed by the hypergeom function to the LegendreP(n,b,x) or Q function?


 

restart

with(PDETools):

infolevel[pdsolve] := 3:

sol[1] := dsolve((1-x^2)*(diff(y(x), x, x))+n(n+1)*y(x) = 0)

y(x) = _C1*(-1+x^2)*hypergeom([3/4+(1/4)*(4*n(n+1)+1)^(1/2), 3/4-(1/4)*(4*n(n+1)+1)^(1/2)], [1/2], x^2)+_C2*(x^3-x)*hypergeom([5/4+(1/4)*(4*n(n+1)+1)^(1/2), 5/4-(1/4)*(4*n(n+1)+1)^(1/2)], [3/2], x^2)

(1)

convert(sol[1], LegendreP)

y(x) = _C1*(-1+x^2)*hypergeom([3/4+(1/4)*(4*n(n+1)+1)^(1/2), 3/4-(1/4)*(4*n(n+1)+1)^(1/2)], [1/2], x^2)+_C2*(x^3-x)*hypergeom([5/4+(1/4)*(4*n(n+1)+1)^(1/2), 5/4-(1/4)*(4*n(n+1)+1)^(1/2)], [3/2], x^2)

(2)

``


Download convert-Legendre.mw

https://math.stackexchange.com/questions/3254765/how-to-convert-a-hypergeom-function-to-the-legendre-function

I just want y(x) to be expressed in the form of LegendreP(n,b,x).

I need help on solving the following PDE by Maple:

https://math.stackexchange.com/questions/3177491/how-to-solve-the-given-partial-differential-equation

I couldn't write the partial differential equation in Mapleprimes so provided the link from somewhere else. Please help. Thank you.

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