10h
awarded Popular Question
11h
awarded Popular Question
Jan
28
accepted Eliminating a nuisance parameter in likelihood ratio test
Jan
12
awarded Supporter
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 $J_n(x)$
Oct
27
revised Summation of an integral involving Laguerre polynomial and Bessel function
fixed omission
Oct
27
asked Summation of an integral involving Laguerre polynomial and Bessel function
Oct
16
revised Approximating two-dimensional convolution
solved the problem
Oct
14
asked Approximating two-dimensional convolution
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
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