- #1

Another1

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\(\displaystyle g(x,t) = e^{(\frac{x}{2})(t-\frac{1}{t})}=\sum_{n=-\infty}^{\infty}J_{n}(x)t^{n}\)

and

\(\displaystyle \left| J_{0}(x) \right|\le 1 \) and \(\displaystyle \left| J_{n}(x) \right|\le \frac{1}{\sqrt{2}} \)

how to show that

1=\(\displaystyle (J_{0}(x))^{2}+2(J_{1}(x))^{2}+2(J_{2}(x))^{2}+...\)

I don't have idea

and

\(\displaystyle \left| J_{0}(x) \right|\le 1 \) and \(\displaystyle \left| J_{n}(x) \right|\le \frac{1}{\sqrt{2}} \)

how to show that

1=\(\displaystyle (J_{0}(x))^{2}+2(J_{1}(x))^{2}+2(J_{2}(x))^{2}+...\)

I don't have idea

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