The Pincherle derivative is implicitly used in Eqn. 2.19 page 13 of “Mastering the master field” by Gopakumar and Gross. The raising and creation operators in the paper are analogous to those for a Laplace-dual Appell sequence, or Dirac-Appell sequence, comprised of the Dirac delta function and its derivatives, formed by taking the inverse Laplace transform of the polynomials of an Appell polynomial sequence.
The fundamental D-A sequence can be defined as the sequence with and and e.g.f. . Another example is provided by OEIS A099174 with the D-A sequence where are the modified Hermite polynomials listed in the Example section of the entry. The modified Hermite polynomials can be characterized several ways: