| http://www.w3.org/ns/prov#value | - In the book, there is a hint saying that for $x$ in the mentioned interval $x \in [ 0, \alpha]$, and using the inequality $\sin x \geqslant x-\frac{x^{3}}{3!}$, we get: $$ \left| n \sin \sqrt{4\pi^2 n^2+x^2} -\frac{x^2}{4\pi} \right| \leqslant \frac{a^2}{4\pi } \left ( 1-\frac{2}{\sqrt{1+\frac{a^2}{4\pi^2 n^2}}+1} \right ) + \frac{n}{3!} \frac{\alpha^6}{8n^3 \pi^3} .$$
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