22 July 2026

Saint Mary Magdalene (1st Century AD)

 

3020. Thoughts and Tricks about UTF (Universal Transcendental Function)

 

Intel FORTRAN Code and Printout of the 731 Transcendental Constants in QUAD Precision (733 Constants including all)

 

22 July 2026

Universal Transcendental Constants, or UTC, are used throughout many of my articles and will continue to be used in future work. For that reason, I think it is useful to have the values of these constants readily available.

Attached to this article are two FORTRAN codes, along with their printouts in QUAD precision. These are older results, originally produced in 2017, but they remain accurate. I ran the programs using Intel FORTRAN and Microsoft Visual Studio 2017, or alternatively using just the Intel compiler and editor. The files, including the printouts and source codes, were edited in 2026.

The Universal Transcendental Function

To begin, let us recall the formula for the Universal Transcendental Function, abbreviated as UTF:

This will be referred to as Equation 1.

Here,  is the number, or index, of the constant. For example:

Since anything raised to the power of zero is equal to 1, this gives:

Therefore:

Another example is:

So:

and:

The Positions of  and

In this system,  and  occupy positions number 8 and 7, respectively.

That means:

or:

Similarly:

or:

Thus, the value of a UTC, or Universal Transcendental Constant, is equal to the value of the UTF when the exponent  in

is equal to the index, or subscript, of that UTC.

For example,   has index 16, so the exponent  in the UTF formula is also 16:

Expressing UTC as Ratios of Powers of  and

Another important observation is that   can be written as:

which gives:

Similarly:

which gives:

Therefore, all UTC values can be expressed as ratios of powers of  and .

Upcoming Articles

The next series of articles will discuss the relation between the Fine Structure Constant, alpha , the anomalous magnetic dipole moment of the electron, , and the anomalous magnetic dipole moment of the muon, .

These quantities are contained in a single, elegant equation, possibly proving the exact result of the Fine Structure Constant:

The Intel FORTRAN code and printouts will be supplied.

Attachments

The following files accompany this article:

1. Intel FORTRAN source code for the UTC calculation
2. Intel FORTRAN source code for the related printout/calculation
3. QUAD precision printout of the 731 Universal Transcendental Constants
4. Additional edited output files, prepared in 2026

 
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