User blog comment:B1mb0w/Beta Function Code Version 1/@comment-24920136-20160424002342/@comment-10262436-20160424100751

Hi. Yes the Beta function will accept any real number input. e.g. surds

b(7^.5,3) = f_2^2(3) + 5

transcendentals

b(e,3) = f_2^2(3) + f_2(3).2 + 1

b(pi,3) = f_{w + 1}(3) + 1

I use Microssoft Excel to calculate the results and like all computer programs, it is limited to about ...

pi = 3.14159265358979

... 14 decimal places precision. Different algorithms can be used to generate any real with finite number of decimal places precision, but it is not really an issue for the Beta Function because all real numbers with a finite number of decimal places will generate unique big numbers using FGH notation. In other words real numbers with infinite number of decimal places precision are not required to access every big number using FGH notation via the Beta Function.

To illustrate this, the following real numbers generate the same big number output as when using pi in the example above.

b(3.14155,3) = f_{w + 1}(3) + 1

b(3.1416,3) = f_{w + 1}(3) + 1

Cheers.