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please answer the question below with complete stepsImage for Show that P l m (0) = (-1)^(l + m)/2 (l + m - 1)!!/(l - m)!!

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These functions are denoted (), where the superscript indicates the order, and not a power of P. Their most straigatforward definition is in terms of derivatives of ordinary Legendre polynomials (m20) The (- 1) factor in this formula is known as the Condon-Shortley phase. Some authors omit it. That the functions described by this equation satisfy the general Legendre differential equation with the indicated values of the parameters E and m follows by differentiating m times the Legendre equation for P d2 dr2 Moreover, since by Rodrigues formula, Pe(r) the Pmt can be expressed in the form (-1)m 2 e 7mPen(o) = (-1)m(1-02)-/2 de+ー(02-1) e+m (-1)m 2%! 772 m/2 (-1)m/2 211! ljk

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