Abstract
Without using product representations or elaborate comparisons of zeros we prove the two key properties of the Bessel function ratioJ p+1 j p+1,1 x/J p j p,1 x that we used to prove the Payne-Pólya-Weinberger conjecture. In these new proofs we use only differential equations and the Rayleigh-Ritz method for estimating lowest eigenvalues. The new proofs admit generalization to other related problems where our previous proofs fail.
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Communicated by B. Simon
Partially supported by FONDECYT (Chile) project number 1238-90
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Ashbaugh, M.S., Benguria, R.D. A second proof of the Payne-Pólya-Weinberger conjecture. Commun.Math. Phys. 147, 181–190 (1992). https://doi.org/10.1007/BF02099533
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DOI: https://doi.org/10.1007/BF02099533