On the bounds for the K?3 form factors

A complete solution is given to a mathematical problem encountered in the search for bounds on the K_?3 scalar form factor. Besides standard analyticity assumptions, the information used is, firstly, the Mathur-Okubo inequality derived from a chiral model, secondly the experimental low-energy $\text{I =}\text{1}\text{2}$, S-wave, Kπ phase shift. Upper and lower bounds are computed, compared with previous bounds, and found to be in agreement with recent experimental data.