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The functional equation
(n-1)fn+1(z) + (n + l)fn-1(z)-2/z(n2-1)fn(z)=0 (1)
can be transformed into the form
φn+1(Z)+ φn-1(Z) = 2n/zφ n( Z ) (2)
by the substitution
fn(Z) = nφn(z). (3)