Expansions of certain inverse factorial series via series and sequence transformations

Key Points

• The aim is to explore expansions of inverse factorial series related to harmonic numbers and derive new expressions for Dirichlet series.
• Investigated generalizations of harmonic numbers and their relationships in series transformations.
• Analyzed the inverse factorial series of binomial, Stirling, and Lah transformations.
• Derived new closed form formulas for inverse factorial series based on p-Stirling numbers.
• New expressions for Dirichlet series associated with hyperharmonic numbers were obtained.
• Relationships between various series transformations were clarified.
• Closed form formulas for certain inverse factorial series were successfully derived.

Abstract