Let , then for any operator ,

is called the Pincherle derivative of . If is a shift-invariant operator, then its Pincherle derivative is also a shift-invariant operator.

Pincherle, S. "Operatori lineari e coefficienti di fattoriali." Alti Accad. Naz. Lincei, Rend. Cl. Fis. Mat. Nat. (6) 18, 417-519, 1933.

Rota, G.-C.; Kahaner, D.; Odlyzko, A. "On the Foundations of Combinatorial Theory. VIII: Finite Operator Calculus." J. Math. Anal. Appl. 42, 684-760, 1973.

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Weisstein, Eric W. "Pincherle Derivative." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PincherleDerivative.html