A New Identity Linking Bernoulli Numbers, Stirling Numbers of the First Kind, and Bessel Numbers of the First Kind

Key Points

• The identity establishes a new link between three mathematical families: Bernoulli, Stirling, and Bessel numbers.
• The connection parallels the classical Stirling–Bernoulli relation, enhancing understanding of these concepts.
• This identity reveals underlying relationships in combinatorial mathematics, offering deeper insights into these number families.
• Replacing Stirling numbers in the classical relation allows for the exploration of new properties and applications.