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I am confused regarding the Legendre Differential Equations' coefficients. In some books its,

$(1-x^2)y''-2xy'+n(n-1)y=0$

and somewhere it is,

$(1-x^2)y''-2xy'+n(n+1)y=0$

what is its correct form?

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  • $\begingroup$ Perhaps both forms are correct. $\endgroup$ Nov 29, 2023 at 10:41
  • $\begingroup$ There is just a shift of the index. The second one is simpler (two less characters to be typed). $\endgroup$ Nov 29, 2023 at 12:20
  • $\begingroup$ Oh, i got it, thanks, n -> n-1 $\endgroup$
    – Ajay Mehra
    Nov 29, 2023 at 12:20

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