Normalized Weyl-type $\star$-product on K\"ahler manifolds

We define a normalized Weyl-type $\star$-product on general K"{a}hler manifolds. Expanding this product perturbatively we show that the cumbersome term, which appears in a Berezin-type product, does not appear at least in the first order of $\mathrm{\hslash }$. This means a normalization factor, which is introduced by Reshetikhin and Takhtajan for a Berezin-type product, is unnecessary for our Weyl-type product at that order.