  We extend some results about shifted Schur functions to the general context
of shifted Macdonald polynomials. We obtain two explicit formulas for these
polynomials: a $q$-integral representation and a combinatorial formula. Our
main tool is a $q$-integral representation for ordinary Macdonald polynomials.
We also discuss duality for shifted Macdonald polynomials and Jack degeneration
of these polynomials.
