{'fraction_non_alphanumeric': 0.02711864406779661, 'fraction_numerical': 0.0, 'mean_word_length': 4.67948717948718, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Is Euler's constant a value of an arithmetic special function?

Euler's constant γ is one of the mathematical constants with the most different analytic representations, probably on par with π. Yet, none of these representations proves that γ is a value of an E-function, a G-function or an M-function at an algebraic point. In fact, it is plausible that no such representation of γ exists with these three arithmetic special functions, and thus the arithmetic nature of γ might not be determined by the powerful Diophantine theorems of Siegel-Shidlovsky, Chudnovsky and Nishioka. Nonetheless, we explain here why certain of these representations show that γ is not far from being a special value of both E-functions and M-functions, while a similar connection to G-functions is still elusive. We also present a new family of series summing to γ, which generalize an identity of Vacca.