I have found two derivatives of the so-called Riccati-Bessel functions in a textbook
$$ (x j_n(x))'=xj_{n-1}(x)-nj_{n}(x)$$ and $$ (x h_n^{(1)}(x))'=x h_{n-1}^{(1)}(x)-n h_n^{(1)}(x)$$
so $j_n$ is the spherical bessel function of the 1st kind and $h_n$ is the spherical hankel function of the first kind.
Since these derivatives differ from what I would assume, I just wanted to ask you whether they are wrong?
Perhaps this is the result of a somewhat different calculation, so maybe he just differentiated the sph. bessel function and not the x in front, but anyway I would be interested if somebody here could check this.
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