Motivated by the hyper-holomorphic case we introduce and study rational functions in the setting of Hida’s white noise space. The Fueter polynomials are replaced by a basis computed in terms of the Hermite functions, and the Cauchy-Kovalevskaya product is replaced by the Wick product.
D. Alpay and D. Levanony. Rational functions associated to the white noise space and related topics. Potential Analysis, vol. 29 (2008) pp. 195-220.