{'fraction_non_alphanumeric': 0.056218057921635436, 'fraction_numerical': 0.0, 'mean_word_length': 5.0, '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}}
Transcendental functions generalizing the exponential integrals

A new set of generalized exponential integrals E(m)(x,v) which arise in linear transport theory are defined, and their asymptotic.and (m), series expansions are developed. The special cases E (x,n), n positive integer, are shown to correspond to the functions E(m)(x) as defined by n C. Kaplan, H. C. Van de Hulst and others. Considerable simplification results for the series development for El n) (x). The connections with the incomplete gamma, the gamma, the psi, the polygamma and the Riemann zeta functions are noted.