Thinh

I could only understand this in the sense that you can obtain

the Euler constant from the harmonic series and ln

Value of irrational numbers cannot be exactly expressed in the form of fraction with integers.

Thinh,

I don't think there is a rule. Some connections ofcourse. An example:

The Riemann z-funktion gives pi*pi/6 for z(2) and it can also be written as a product over the primes. A proof is on wikipedia:

https://en.m.wikipedia.org/wiki/Proof_of_the_Euler_product_formula_for_the_Riemann_zeta_function

Kind regards

Dear George, can you explain what you mean by density-type arguments? Thank you in advance.

Yes, Jens Fischer is right. I am also confused with this concept

definately not scientific constants

Mathematical constants maybe in the sense of Lena or mine

The concept is that any irrational number can be approached by

some adequate rational number within some prefixed small error.

ie. a rational number of the form p/q with large enough p and q

Or as stated by Peter, that the rationals can form a dense set.,there are an arbitrary large number in any small interal.

Some infinite series of rationals added together can sometimes be considered to give the irrational number, in Lenas example, if the series is convergent.

Ok, I guess that "density-type arguments" means that ratios of primes "form a dense set in the reals". Makes sense.