Written: March 25, 2019
Dear Doron
I have read with pleasure and interest your paper about Ruehr, this morning on the ArXiv!
I both agree and disagree with you, smiles.
I do agree that your routine proofs are quite easy and much better than any n-page long circuitous proof! On the other hand both claims (the one on integrals and the one on binomial sums) had already been proved separately by others --again not as immediate as the super-speedy routine proof, and one might ask about the real interest of trying to guess what Ruehr meant.
Of course, as you write, the question is more what Ruehr had in mind, and this is truly only of psychological and/or literary interest. I must confess that this was sort of my true motivation: after having tried hard to find what he meant (and after have asked colleagues who did not succeed either --or may be who did not really care, smiles), I could not resign and abandon this question unsolved.
By the way, I guess that another paper on Ruehr's identities that I wrote can be proved by your approach?