The purpose of Series Math Study (SMS) website is to explore and develop the beauty of series formulas that have connections to special mathematical constants. Some series can be used to calculate ever more accurate values of some special math constants as the desire that has challenged mathematicians for many centuries.
Submitted by admin on Wed, 01/03/2024 - 10:08pm
2/20/2026
We’re pleased to announce the release of our new book entitled "Embarking on Adventurous Journeys Through Some Subjects in Pure Mathematics - Part II," which covers two new subjects: Extension of Fundamental Trigonometric and Hyperbolic Functions, and Unraveling the Mystery of the Riemann Hypothesis: Toward a Complete Proof. This book is 100% free to read, just click on download and enjoy!
We present a new subject that is somewhat sensitive in the field of mathematics: the intentional effort to reconsider the necessity of extending elementary trigonometric and hyperbolic functions from one variable to two variables, despite the fact that the set of one variable elementary functions is already adequate for the analysis of any object in the universe. It it quite challenging to develop new two variable elementary functions; therefore, we extend all elementary trigonometric and hyperbolic functions from one variable to two variables while maintaining the fundamental mathematical essence of these functions.
The second subject elucidates the enigma of the Riemann Hypothesis, identifies a saturation constant (6.28983598...), and demonstrates that no nontrivial zeros lie beyond this constant within the critical strip but off the critical line.
The book can be downloaded here. The Python scripts are also available for download, allowing users to examine the graphs, compute constant value and solve numerical equations.
Notice that we present our work as a narrative of self-discovery, letting ideas unfold naturally with the journey of insight. The book is intended for readers who love mathematics and are comfortable with fundamental concepts.
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