{'fraction_non_alphanumeric': 0.01338199513381995, 'fraction_numerical': 0.0, 'mean_word_length': 5.745901639344262, '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}}
Spectral transformations and generalized Pollaczek polynomials

The Christoffel and the Geronimus transformations of the classical orthogonal polynomials of a discrete variable are exploited to construct new families of the generalized Pollaczek polynomials. The recurrence coefficients un, bn of these polynomials are rational functions of the argument n. The (positive) weight function is known explicitly. These polynomials are shown to belong to a subclass of the semi-classical orthogonal polynomials of a discrete variable. We illustrate the method by constructing a family of the modified Charlier polynomials which are orthogonal with respect to a perturbed Poisson distribution. The generating function of these polynomials provides a nontrivial extension of the class of the Meixner-Sheffer generating functions.