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Let \( g(x)=\log f(x) \) where \( f(x) \) is twice differentiable
P positive function on \( (0, \infty) \) such that \( f(x+1)=x f(x) \).

W.
Then, for \( N=1,2,3 \ldots g^{\prime \prime}\left(N+\frac{1}{2}\right)-g^{\prime \prime}\left(\frac{1}{2}\right)= \)
(A) \( -4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots+\frac{1}{(2 N-1)^{2}}\right\} \)
(C) \( -4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots .+\frac{1}{(2 N+1)^{2}}\right\} \)
(B) \( 4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots .+\frac{1}{(2 N-1)^{2}}\right\} \)
(D) \( 4\left\{1+\frac{1}{9}+\frac{1}{25}+\ldots .+\frac{1}{(2 N+1)^{2}}\right\} \)
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