4000. 7. Derivation of the General Formula for Constants of Cosmology and Quantum Mechanics – Part II

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Article Category / Series:
Book 6 – Derivation of the General Formula for Constants of Cosmology and Quantum Mechanics

Article Number: 4000.7

Article Title: Derivation of the General Formula for Constants of Cosmology and Quantum Mechanics – Part II

Publication Date:
23 September 2017 AD — Feast of St Pio and St Linus

Last Edited:
11 September 2026 — Feast of Sts. Protus & Hyacinth; St. Adelphus; St. Paphnutius

Author:
Andrew Joseph Yanthar-Wasilik

2. Dedication

This article is dedicated to God the Eternal Father, the Creator of the Universe and Beyond.

3. Introduction

Purpose of This Article

This article continues the derivation begun in Part I of Book 6 and seeks a general formula for constants discussed in the previous work:

Book 5: Integer Formula for Dimensionless Coupling Constants of Fundamental Forces.

The general constant is denoted by alpha, α, as there may be constants beyond those presently known.

4. Table of Contents

1. Exponent Main: ExpM
2. Derivation of Exponent D
3. Transcendental Function FT
4. Derivation of Partial Exponent ExpP
5. Denominator Sequence for α
6. General Formula for α
7. Definitions of A, B, C, and ExpM
8. Obtaining α⁻¹ and α
9. Application to Any Value of x
10. Conclusion and Next Section

1. Exponent Main: ExpM

The Exponent Main, ExpM, derived in Part I, is:

Equation EM

2. Derivation of Exponent D

2.1 Partial Sequence

2.2 General Formula

Equation D

Or:

Explanation

Exponent D is used to calculate the value of the function at .

3. Transcendental Function FT

Having obtained exponent D, the transcendental function at point  is:

Equation FT

4. Derivation of Partial Exponent ExpP

4.1 Initial Sequence Terms

4.2 Derivation of y

The sequence component is represented by:

This corresponds to Equation A.

Equation A

4.3 Addition of x and y

4.4 General Formula for ExpP

Equation EP

5. Denominator Sequence for α

The denominator arises from the expression:

Equation αE

5.1 Example Terms

Constant	Denominator Term
C16
C17
C1

5.2 First Component

The first partial sequence is:

It is represented by:

 

5.3 Second Component

5.4 Combined Denominator Expression

Taking the reciprocal gives the corresponding product factor:

6. General Formula for α

6.1 Formula for

Equation α

7. Definitions of ExpM, A, B, and C

7.1 Exponent Main

7.2 Component A

Equation A

7.3 Component B

Equation B

7.4 Component C

Equation C

8. Obtaining α⁻¹ and α

To Obtain

Square Equation α:

To Obtain α

Take the reciprocal:

9. Scope of x

The variable  may be any number, including:

• Integer values
• Real numbers
• Complex numbers
• Algebraic numbers
• Transcendental numbers

 

According to the article, the general equation for  permits calculation of coupling constants and potentially other quantities not yet known.

10. Conclusion

A shorter expression for ExpM and α may be possible, though the article states that deriving one could be difficult and may require professional mathematical work.

The article’s next section is intended to present:

Graphs of the universal equation.

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Book 6, Part I — Derivation of the Exponent Main, ExpM

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Graphs of the Universal Equation

Related Article:
Book 5 — Integer Formula for Dimensionless Coupling Constants of Fundamental Forces