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math.CO2025
Normal Ordering in the Algebra Generated by and and a Combinatorial Generalization of Bessel Numbers
Abdelhay Benmoussa
We investigate the algebra generated by the operators and , which satisfy the commutation relation \[ [\mathrm{I},x] = \mathrm{I}x - x\mathrm{I} = - \mat…
math.CO2025
Normal Ordering and Bessel Numbers with Integral Operators
Abdelhay Benmoussa
We derive a normal ordering formula for the operator \((xI)^n\), where \(I\) denotes the Volterra operator. The resulting coefficients are shown to coincide with the Bessel numbers…