Life of Pi. About numbers.

[questfortruth]

Or maybe the number Pi cannot be expressed in terms of analytic functions but only in an infinite series. In such a case, what then is Pi called? Is there a special name for such numbers? What is the name of an irrational number that cannot be expressed through elementary functions? For example, Pi is not equal to the natural logarithm of a yet unknown rational number.

Suppose that exp(1)=ln(A). Is known that exp(1)=e is transcendental. But it is not known is A rational or irrational. If A is not rational, how e would be called? Super-transcendental?

 

[exchemist]

Or maybe the number Pi cannot be expressed in terms of analytic functions but only in an infinite series. In such a case, what then is Pi called? Is there a special name for such numbers? What is the name of an irrational number that cannot be expressed through elementary functions? For example, Pi is not equal to the natural logarithm of a yet unknown rational number.

"Transcendental", I think.

e is another example.

Transcendental number - Wikipedia

 

[questfortruth]

"Transcendental", I think.

Suppose that exp(1)=ln(A). Is known that exp(1)=e is transcendental. But it is not known is A rational or irrational. If A is not rational, how e would be called? Super-transcendental?

 

[Polymath257]

Or maybe the number Pi cannot be expressed in terms of analytic functions but only in an infinite series. In such a case, what then is Pi called? Is there a special name for such numbers? What is the name of an irrational number that cannot be expressed through elementary functions? For example, Pi is not equal to the natural logarithm of a yet unknown rational number.

Pi is 4 times the inverse tangent of 1.

Alternatively, pi is -i*log(-1), where the principal logarithm is taken.

Suppose that exp(1)=ln(A). Is known that exp(1)=e is transcendental. But it is not known is A rational or irrational. If A is not rational, how e would be called? Super-transcendental?

As far as I know, there is no special terminology for a number whose logarithm is transcendental or even irrational.

 

[Watchmen]

It was a great movie.