{'fraction_non_alphanumeric': 0.046875, 'fraction_numerical': 0.0, 'mean_word_length': 5.284313725490196, '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}}
Gaussian-hyperbolic Numbers Containing Pell and Pell-Lucas Numbers

In this study, we define a new type of Pell and Pell-Lucas numbers which are called Gaussian-hyperbolic Pell and Pell-Lucas numbers. We also give negaGaussian-hyperbolic Pell and Pell-Lucas numbers. More-over, we obtain the Binet’s formula, generating function formula, d’Ocagne’s identity, Catalan’s identity, Cassini’s identity and some sum formulas for these new type numbers. Some algebraic proporties of Gaussian-hyperbolic Pell and Pell-Lucas numbers are investigated. Futhermore, we give the matrix repre-sentation of Gaussian-hyperbolic Pell and Pell-Lucas number.