{'fraction_non_alphanumeric': 0.014112903225806451, 'fraction_numerical': 0.0, 'mean_word_length': 5.060975609756097, '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}}
On the Lanczos limit formula

In this article we derive a limit representation for a class of analytic functions, which generalizes Lanczos limit formula for Gamma function. This limit representation is valid in the entire complex plane, and it is shown to be an analogue of the Euler–Maclaurin summation formula. As examples we provide approximations to Gamma function and Riemann zeta function, and as a corollary we derive characterization of the nontrivial zeros of the Riemann zeta function.