Proves a universal identity for umbral operators and fully characterizes a subclass satisfying a simplified version of the identity, with examples from umbral calculus.
On formulas and fractional exponents for umbral operators
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abstract
We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads naturally to a definition of fractional exponents of umbral operators. Third, its proof synthesizes a broad range of existing results in operational calculus and highlights their combined effectiveness. As an illustration, we obtain a new and natural extension of the Laguerre polynomials.
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math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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A general identity for umbral operators and a special subclass
Proves a universal identity for umbral operators and fully characterizes a subclass satisfying a simplified version of the identity, with examples from umbral calculus.