{"id":{"repo_id":"must-thes","oai_identifier":"oai:scholarsmine.mst.edu:doctoral_dissertations-3562"},"canonical_url":"https://search.dev.ndltd.org/etd/must-thes/oai:scholarsmine.mst.edu:doctoral_dissertations-3562","repository":{"repo_id":"must-thes","name":"Missouri University of Science and Technology","base_url":"https://scholarsmine.mst.edu/do/oai/"},"display":{"title":"A harmonic M-factorial function and applications","abstract":"\"We offer analogs to the falling factorial and rising factorial functions for the set of harmonic numbers, as well as a mixed factorial function called the M-factorial. From these concepts, we develop a harmonic analog of the binomial coefficient and an alternate expression of the harmonic exponential function and establish several identities. We generalize from the harmonic numbers to a general time scale and demonstrate how solutions to some second order eigenvalue problems and partial dynamic equations can be constructed using power series built from the M-factorial function\"--Abstract, page iii.","abstract_html":""We offer analogs to the falling factorial and rising factorial functions for the set of harmonic numbers, as well as a mixed factorial function called the M-factorial. From these concepts, we develop a harmonic analog of the binomial coefficient and an alternate expression of the harmonic exponential function and establish several identities. We generalize from the harmonic numbers to a general time scale and demonstrate how solutions to some second order eigenvalue problems and partial dynamic equations can be constructed using power series built from the M-factorial function"--Abstract, page iii.","abstract_has_math":false,"creators":["Brigham, Reginald Alfred, II"],"institution":"Missouri University of Science and Technology","degree_name":"Ph. D. in Mathematics","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T03:18:26Z","subjects":["Binomial Coefficient","Eigenvalue","Factorial","Harmonic Numbers","Time Scales","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/2557","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Brigham, Reginald Alfred, II"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Mathematics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Missouri University of Science and Technology"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Binomial Coefficient","Eigenvalue","Factorial","Harmonic Numbers","Time Scales","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsmine.mst.edu/doctoral_dissertations/2557"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["\"We offer analogs to the falling factorial and rising factorial functions for the set of harmonic numbers, as well as a mixed factorial function called the M-factorial. From these concepts, we develop a harmonic analog of the binomial coefficient and an alternate expression of the harmonic exponential function and establish several identities. We generalize from the harmonic numbers to a general time scale and demonstrate how solutions to some second order eigenvalue problems and partial dynamic equations can be constructed using power series built from the M-factorial function\"--Abstract, page iii."]},{"key":"dc:title","label":"Title","values":["A harmonic M-factorial function and applications"]}]}],"canonical_facts":{"dc:creator":["Brigham, Reginald Alfred, II"],"dc:description.abstract":["\"We offer analogs to the falling factorial and rising factorial functions for the set of harmonic numbers, as well as a mixed factorial function called the M-factorial. From these concepts, we develop a harmonic analog of the binomial coefficient and an alternate expression of the harmonic exponential function and establish several identities. We generalize from the harmonic numbers to a general time scale and demonstrate how solutions to some second order eigenvalue problems and partial dynamic equations can be constructed using power series built from the M-factorial function\"--Abstract, page iii."],"dc:identifier":["https://scholarsmine.mst.edu/doctoral_dissertations/2557"],"dc:subject":["Binomial Coefficient","Eigenvalue","Factorial","Harmonic Numbers","Time Scales","Mathematics"],"dc:title":["A harmonic M-factorial function and applications"],"dc:type":["Dissertation - Open Access"],"thesis:degree_name":["Ph. D. in Mathematics"],"thesis:institution_name":["Missouri University of Science and Technology"]},"updated_at":"2026-07-24T03:18:26Z"}