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    $\begingroup$ can you comment as to if there is a closed form formula just for the sign of $\langle n'l'|r^k|nl\rangle$? This is, I guess, a property of the $I$ function? $\endgroup$ Commented Nov 30, 2023 at 16:46
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    $\begingroup$ @Jagerber48 I’m not aware of one. $\endgroup$ Commented Nov 30, 2023 at 17:36