## Transcendental Constants - Introduction.

#### Andrew Yanthar-Wasilik

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

**Abstract.** This paper contains introduction to Transcendental Constants similar to e, π and derived from them. 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 – Transcendental Function - Introduction.**

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

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

#### and

####

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

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

####

#### calculate parameter “a”

####

#### substituting numerical values

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

####

#### into Eqn. (3)

####

#### gives

####

#### So the final formula is:

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

#### Final formula 2nd version is

####

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

**2. Graph of 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 most important Transcendental Constants are in range of 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 ie, from to .

**3. Some of the properties of 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?

#### eg.,

####

#### – 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 graph of ln(y) vs x will give straight line, and it does).

####

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

####

####

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

#### for x = 0

####

#### and

#### c) and linear equation is

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

#### a) derivative

####

#### value of coefficient in derivative

#### b) integral

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

#### (3)Next Books will be describing in depth properties of Transcendental Function

*Fig. 1 Graph of Transcendental Function*

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