3 papers
math.CO2026
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…
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.GM2025
A New Identity Linking Bernoulli Numbers, Stirling Numbers of the First Kind, and Bessel Numbers of the First Kind
Abdelhay Benmoussa
We establish a new identity linking Bernoulli, Stirling (first kind), and Bessel (first kind) numbers: \[ \sum_{k=0}^{n} 2^{\,n-k}\,s(n,k)\,B_k \;=\; \sum_{k=0}^{n} b(n,k)\,\frac{(…