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I am implementing the scattering of dielectric sphere under electromagnetic plane wave. The expression of the field contain [tex]\frac{P_n^1(\cos\theta)}{\sin\theta}[/tex] and[tex]\sin\theta P_n^1'(\cos\theta)[/tex], where the derivative is with respect to the argument.

These two terms are giving me difficulty when [tex]\theta=0[/tex] or [tex]\theta=\pi[/tex].

When [tex]\theta=\pi[/tex], in one book (Harrington's Time-Harmonic Electromagnetic Fields), both terms are stated to be

[tex]\frac{(-1)^n n(n+1)}{2}[/tex] on Page 295. In another book (Balanis' Advanced Electromagnetic Engineering), both terms are equal [tex]-\frac{(-1)^n n(n+1)}{2}[/tex].

I don't know which one is correct. Could someone tell me how could I evaluate these two expressions at [tex]\theta=0, \pi[/tex]. Thank you.

kzhu

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# Evalute expression of associated Legendre's polynomial

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