A Bessel function based proof that the Euler-Mascheroni constant is transcendental
A strictly monotonically increasing sequence of transcendental numbers is constructed, which converges to the Euler-Mascheroni constant. This proves that the constant is irrational.
The essential tools for this proof are Bessel functions, their Mellin transforms, and the technique R. P. Brent used in his paper "asymptotic expansions inspired by Ramanujan", (BrR).
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