Nilpotent operators truncate hypergeometric series to polynomials of degree at most the index minus one, and analytic functions reduce exceptional-point Jordan depth by a factor tied to the function's lowest-order non-constant term.
Znojil, Intrinsic exceptional point: a challenge in quantum theory, Foundations 5 (2025), Article 8
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Hypergeometric Functions of Nilpotent Operators: Functional Collapse and Structural Depth at Exceptional Points
Nilpotent operators truncate hypergeometric series to polynomials of degree at most the index minus one, and analytic functions reduce exceptional-point Jordan depth by a factor tied to the function's lowest-order non-constant term.