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

**3/3/2024**

We are pleased to inform you that the book titled "Embarking on Adventurous Journeys Through Some Subjects in Pure Mathematics" has been published on Amazon at this link, https://www.amazon.com/dp/B0CWF7FZWH (kindle readers - https://www.amazon.com/dp/B0CW1KVN76 ). The publication focuses on two elementary mathematical subjects: the exploration of nested radicals and algebraic identities, and the art of solving polynomial equations using of trigonometric and hyperbolic trigonometric functions. The first subject unveils beautiful nested radical identities in algebra, along with essential known formulas in mathematics. Meanwhile, the second subject unveils an innovative approach to solving polynomial equations, encompassing quadratic to quartic and other higher order solvable equations, by utilizing trigonometric and hyperbolic trigonometric functions. Since this book is on Amazon now, it will be available for free access on SMS website after 90 days. Readers can download it at no cost. Specifically, the Kindle book version is available for free on Amazon from March 17th to March 21st.

Below are several algebraic identities and solutions to cubic, quartic, special quintic, and higher-degree equations, encompassing numerous findings presented in the book. They signify remarkable breakthroughs, characterized by their refinement and elegance, unseen on this website before.

**1. Nested Radicals**

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where a, b, A, B and x are real numbers.

**2. Complex Fourth Root**

,

where a and b are real numbers.

**3. Radical expression for the quarter of the lemniscate sine**

**4. Solution to the cubic equation**

**5. Solution to the quartic equation**

**6. Solution to the special quintic equation**

**7. Solution to the special sextic equation**

**8. Solution to the special septic equation**

**9. Solution to the special octic equation**

**10. Solution to the special 9th degree equation**

Some formulas and solutions presented above are incomplete. For further details, please refer to the book.