Functions and Analysis

    

Analytic Derivation and Computational Visualization of Five Novel Series

Authors: Marciano L. Legarde

The rigorous analysis of infinite series remains a fundamental driver of discovery in both real and complex analysis, often revealing unique functional representations and essential constants. This paper investigates five novel series, providing a comprehensive analysis of their convergence properties, closed-form expressions, and functional relationships. Utilizing Python-based numerical simulations, we visualize the asymptotic behavior of partial sums through 3D mapping and phase plots. Analytical results demonstrate that these series exhibit significant connections to the Riemann and Hurwitz Zeta functions. These findings suggest non-trivial relationships within the properties of special functions, offering potential insights into open theoretical problems such as the Riemann Hypothesis.

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[v1] 2025-11-30 22:33:18

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