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 P0 – plugging in point 

 

into Eqn. (3) 

 

gives 

 

So the final formula is: 

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

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

Final formula 2nd version is 

 

or, substituting the transcendental constants C0 for P0 

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, al 

 

 

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

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

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

Fig. 1 Graph of Transcendental Function

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

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