Derivation of an Infinite Product Representation for the Factorial (x!) Using Sum-and-Difference Symmetric Structures

Key Points

• The aim is to derive a new representation for the factorial function using infinite products and symmetric structures.
• Develop mathematical equations involving infinite products.
• Incorporate sum-and-difference symmetric structures in the derivation.
• Analyze the convergence and properties of the resulting function.
• A new infinite product formula for the factorial is established.
• The derived representation shows convergence properties.
• The use of symmetric structures enhances understanding of factorial behavior.

Abstract