#### Andrew Yanthar-Wasilik

#### Ottawa, Ontario, Canada 2003-2016

**Abstract.** This paper introduces Universal Transcendental Constants similar to e, π and derived from them. The following books deal with properties of the Transcendental Function, such as index and subscript math, applications in Mathematics, Theology, Philosophy, Quantum Physics, and Cosmology.

**Book1 – Universal Transcendental Function - Introduction.**

**1. How to derive the equation of the Universal Transcendental Function** – once you realize that π is at position “8” at the x-axis and e is at position “7” on the x-axis, the formula can be derived for the whole family of Transcendental Functions. There may be as well other placements of the constants π and e, but I believe I chose the most precise and most elegant.

#### a) We use 2 points on the X-Y plane (1):

#### and

#### – this selection gives the most straightforward relation between Transcendental Constants on Y-axis and Integers on X-axis.

#### b) Given the general equation of the exponential function

#### calculate parameter “a”

#### substituting numerical values

#### c) Solving for parameter P_{0} – plugging in a point

#### into Eqn. (3)

#### gives

#### So the final formula is:

#### (1) For a detailed procedure for finding the equation of the exponential function

#### visit the page of Mr. William Cherry http://wcherry.math.unt.edu/math1650/exponential.pdf

#### The final formula 2nd version is

#### or, substituting the transcendental constants C_{0} for P_{0}

**2. Graph of the Universal Transcendental Function FT (see Fig. 1) **

#### a) Substituting numerical values for x in Eqn. (9) or (10)

#### gives

#### etc., (for other values of x and FT (x) see files - “constants UP.pdf” and “constants DOWN.pdf”), so the graph can be easily plotted. I think that the most important Transcendental Constants are in the range of **C**_{-1} to giving 19 constants. But two of them that is and are “out of our physical universe”, so we are left with 17 Transcendental Constants, i.e., from to .

_{-1}

**3. Some of the properties of the Universal Transcendental Function FT **

#### a) When using Integers for x values, we get precise constants such as: for x=7, we get C7 = e, for x=8, we get C8 = π, for x=0, we get C0, for x=17, we get C17, etc. (In the next books more about index properties of this function).

#### b) To be proven – are all the other constants apart from e and π also transcendental?

#### c) To be proven – are the constants for real values of x are also transcendental?

#### E.g.,

#### – is this transcendental?

**4. Finding the equation of the straight line of ln(y) versus x** (if Eqn. (9,10, and 11 are exponential, then the graph of ln(y) vs. x will give a straight line, and it does).

#### a) calculating slope, a_{l}

#### b) calculating y-intercept, b

#### for x = 0

#### and

#### c) and the linear equation is

**5. Some of the other properties of the Universal Transcendental Function (2)(3)**

#### a) derivative

#### value of the coefficient in derivative

#### b) integral

#### (2) Check WolframAlpha for this and more interesting properties at

#### (enter the equation 10 into the WolframAlpha calculators at http://www.wolframalpha.com/calculators/derivative-calculator/

#### (3) Next Books will describe in-depth properties of the Universal Transcendental Function

Return to the Syllabus >>> 132. Syllabus of the course – “Voyage through God’s Universe (Cosmos and beyond) according to St. Hildegard von Bingen and others, with the help of Mathematics, Cosmology and Quantum Mechanics."

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