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 Mar 26 awarded Popular Question Mar 12 awarded Popular Question Feb 8 awarded Popular Question Dec 19 accepted Simpler proof of an integral representation of Bessel function of the first kind $J_n(x)$ Dec 19 comment Simpler proof of an integral representation of Bessel function of the first kind $J_n(x)$ Yup, I had the same substitutions in mind, except into (2) to show (1). It was really simple once recalled that $e^{in\tau}$ has a period of $2\pi$ over angle $\tau$ for integer $n$. Didn't get around to updating my post, but you should still get the credit for reminding me of that. :) Dec 19 comment Simpler proof of an integral representation of Bessel function of the first kind $J_n(x)$ Ahhh -- I think I got it! Of course, $e^{in\tau}$ has a period of $2\pi$ as long as $n$ is an integer. Since cosine also has a periodic of $2\pi$, everything works! Thank you, I'll update my post either tonight or tomorrow. Dec 18 comment Simpler proof of an integral representation of Bessel function of the first kind $J_n(x)$ Unfortunately, I am not very strong at solving differential equations (having never taken a course on them), but I'll look into this one. I tried the substitution that you mentioned, but couldn't get it to work, since I couldn't find a way to get the right limits of the integral... Dec 18 asked Simpler proof of an integral representation of Bessel function of the first kind $J_n(x)$ Nov 17 awarded Popular Question Nov 4 awarded Popular Question Oct 16 revised Approximating two-dimensional convolution solved the problem Oct 14 asked Approximating two-dimensional convolution Oct 12 awarded Popular Question Oct 5 accepted Equation involving an error and Gaussian functions Oct 5 accepted Extension of the convolution theorem Oct 3 awarded Nice Question Oct 2 revised Fourier transform of a truncated Gaussian function typo Sep 30 comment Equation involving an error and Gaussian functions You are absolutely correct, the resolution on my graph wasn't high enough. The positive solution is clearly not $x=1$, and, yes, differentiating both sides makes no sense... Sep 30 revised Equation involving an error and Gaussian functions updated per deleted comment Sep 30 asked Equation involving an error and Gaussian functions