Functions and Analysis

2511 Submissions

[2] viXra:2511.0151 [pdf] submitted on 2025-11-30 22:33:18

Analytic Derivation and Computational Visualization of Five Novel Series

Authors: Marciano L. Legarde
Comments: 17 Pages. (Note by viXra Admin: Please cite listed scientific references and submit article written with AI assistance to ai.viXra.org)

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.
Category: Functions and Analysis

[1] viXra:2511.0138 [pdf] submitted on 2025-11-27 12:45:45

Short Note: Trigonometric Interpolation for 2N Points

Authors: Andrej Liptaj
Comments: 3 Pages.

The construction of a trigonometric interpolant for an even number of interpolated points is not unique. To resolve this, we propose to minimize the amplitude of the highest-frequency term, which leads to the Gauss interpolation formula.
Category: Functions and Analysis