A New Series Expression and Convergence Characteristics of the Riemann Zeta Function Using Binomial Expansion

Key Points

• This work aims to explore a new series expression for the Riemann zeta function and its convergence properties.
• Develop a series expression using binomial expansion.
• Analyze convergence characteristics of the presented series.
• Apply mathematical analysis to validate findings.
• Introduced a new series expression for the Riemann zeta function.
• Demonstrated favorable convergence characteristics compared to existing methods.