prove that $\int_0^1\left(\frac{tJ_o\left(xt\right)}{\sqrt{\left(1+t^2\right)}}\right)dt=\frac{\sin x}{x}$
How can I solve this equation? Can't find an example like this.Thanks in advanced to all!!
2026-04-03 01:26:59.1775179619
How can I solve this Bessel Integration?
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It is false.
In the picture below I plotted $y=\frac{\sin x}{x}$ in blue and $f(x)=\int_0^1 \frac{t J_0(x t)}{\sqrt{t^2+1}} \, dt$ in orange.