It is shown in two different derivations that a discussion of the associated Legendre functions can be based on the well-known pure-recurrence relation between associated Legendre's functions, ulm(x)⁠,
(l+1−m)ul+1m(x)−x(2l+l)ulm(x)+(l+m)ul−1m(x) = 0
, provided the proper “boundary conditions”
Pll(x) = [(2l)!/l!2l](1 − x2)12l
,
Qll(x) =thinsp;(1+x2)12l(dlQl(x)/dxl)
, are imposed.
Topics
Recurrence relations
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© 1963 American Association of Physics Teachers.
1963
American Association of Physics Teachers
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