We give an explicit formula for the weight spaces in certain simple
modules over an affine Hecke algebra.
The modules to which our formula applies are those containing a weight whose hyperbolic part has Weyl group stabilizer generated by simple reflections.
The formula is given in terms of partial derivatives of harmonic polynomials.
It applies to Hecke algebras with unequal parameters, and that is the main novelty.
For equal parameters, the formula was given in my Crelle paper (1994).
The more general version given here arose from the needs of my paper on formal degrees in exceptional groups.