{"id":{"repo_id":"uab","oai_identifier":"oai:digitalcommons.library.uab.edu:etd-collection-8008"},"canonical_url":"https://search.dev.ndltd.org/etd/uab/oai:digitalcommons.library.uab.edu:etd-collection-8008","repository":{"repo_id":"uab","name":"University of Alabama Birmingham","base_url":"https://digitalcommons.library.uab.edu/do/oai/"},"display":{"title":"The Convergence of a Sequence of Functions Defined by Radicals.","abstract":"In the study of Real Analysis one problem which is often presented is to show that for x > 0, the sequence ✓x, √x + √x, ..., converges to a limit function and to determine the limit function. Since the limit function may be expressed as the positive solution of a quadratic equation, a question arises as to the behavior of similar sequences with radicals of degree greater than two.","abstract_html":"In the study of Real Analysis one problem which is often presented is to show that for x > 0, the sequence ✓x, √x + √x, ..., converges to a limit function and to determine the limit function. Since the limit function may be expressed as the positive solution of a quadratic equation, a question arises as to the behavior of similar sequences with radicals of degree greater than two.","abstract_has_math":false,"creators":["Cooper, Eugene Pinkston"],"institution":null,"degree_name":null,"degree_level":"Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1975,"date_issued":"1975-01-01T08:00:00Z","date_published":"1975-01-01T08:00:00Z","updated_at":"2026-07-24T05:05:33Z","subjects":["Positive solution","Quadratic equation","Positive integer","Monotonic sequence"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.library.uab.edu/etd-collection/7016","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Cooper, Eugene Pinkston"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Positive solution","Quadratic equation","Positive integer","Monotonic sequence"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.library.uab.edu/etd-collection/7016"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In the study of Real Analysis one problem which is often presented is to show that for x > 0, the sequence ✓x, √x + √x, ..., converges to a limit function and to determine the limit function. Since the limit function may be expressed as the positive solution of a quadratic equation, a question arises as to the behavior of similar sequences with radicals of degree greater than two."]},{"key":"dc:title","label":"Title","values":["The Convergence of a Sequence of Functions Defined by Radicals."]}]}],"canonical_facts":{"dc:creator":["Cooper, Eugene Pinkston"],"dc:description.abstract":["In the study of Real Analysis one problem which is often presented is to show that for x > 0, the sequence ✓x, √x + √x, ..., converges to a limit function and to determine the limit function. Since the limit function may be expressed as the positive solution of a quadratic equation, a question arises as to the behavior of similar sequences with radicals of degree greater than two."],"dc:identifier":["https://digitalcommons.library.uab.edu/etd-collection/7016"],"dc:subject":["Positive solution","Quadratic equation","Positive integer","Monotonic sequence"],"dc:title":["The Convergence of a Sequence of Functions Defined by Radicals."],"thesis:degree_level":["Thesis"]},"updated_at":"2026-07-24T05:05:33Z"}