For those of us who are fluent in various math areas but not this one (whatever it is), could you please explain what the problem is?
E.g., what is the gamma constant, and perhaps can your very dense limit expression be broken down a bit?
Thanks.
Also known as the Euler–Mascheroni constant, gamma is a mathematical constant that appears in calculus and number theory. It is defined as the limit of the difference between the harmonic series and the natural logarithm, so one of its expressions is:
gamma = lim (n -> infinity) [(sum from k=1 to k=n (1/k)) - ln(n)].
Despite its widespread occurrence, it is not known whether gamma is rational, irrational, or transcendental—this remains an open question in mathematics.
This constant arises in many areas, and there are numerous expressions for gamma listed here:
https://mathworld.wolfram.com/Euler-MascheroniConstant.html.
I examined the expressions on this page and noted that they involve several advanced concepts, such as:
Euler's number (e), the gamma function, logarithms, pi, complex numbers, prime numbers, factorials, the floor function, integrals, the Riemann zeta function, double series, and nested summations.
Hoping to find a simpler expression that avoids these complexities, I sought to derive a novel representation of gamma that might make it easier to address certain mathematical questions. My journey to the proposed limit is documented here:
https://www.desmos.com/calculator/zgl1vprgdf.
