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Bounds on the expansion coefficients of the strangeness changing $K\pi$ formfactors were derived recently from analyticity and unitarity, using as inputsuitable correlation functions calculated by perturbative QCD in the Euclidianregion. We investigate two types of invariant amplitudes and theircorresponding dispersion relations, and show that they lead to similar resultsfor the shape of the vector and scalar $K_{\ell 3}$ form factors.

QCD Correlation Functions and the Shape of $K_{\ell 3}$ Form Factors