{"id":"e-0a6ae27a6cba0695","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-6cb9b08f268a058b","premise_count":0,"theorem":"L. L. Liu and Y. Wang, Adv. Appl. Math. 38 (2007) 542-560, Theorem 2.1 and Corollary 2.4 (A unified approach to polynomial sequences with only real zeros; the lag row as the interlacer, b_n = 0), weak interlacing of consecutive rows, with nonnegativity of the coefficients replaced, where a root region is certified, by an exact root-location induction","lean_route":null,"lean_declarations":["RealRooted.threeTerm_interlaces_of_window"],"certificate_hash":"36a51476a79112e4f766499aa6d4fbfda8599c2a9e0d9121129205373af630b1","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"theorem_check","certificate_raw_size":3538,"certificate_compressed_size":1198,"conclusion_name":"Matrix inverse of triangle A001497 of Bessel polynomials, read by rows; essentially the same as triangle A096713 of modified Hermite polynomials.","claims":[{"claim":"real_rooted","from_index":1,"region":{"lower":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[],"cited_by":[{"node_id":"n-6cb9b08f268a058b","claim":"real_rooted"},{"node_id":"n-6cb9b08f268a058b","claim":"one_signed_coefficients"},{"node_id":"n-6cb9b08f268a058b","claim":"interlacing"}]}