 By extension, the holonomic function "f" is said to be of order "r" when an annihilating operator of such order exists.A sequence formula_16 is called "P-recursive" (or "holonomic") if there exist polynomials formula_17 such that

holds for all "n".This can also be written as formula_19 where

and formula_21 the shift operator that maps formula_22 to formula_23.