{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:42:03Z","timestamp":1750308123819,"version":"3.41.0"},"reference-count":24,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[1983,5,1]],"date-time":"1983-05-01T00:00:00Z","timestamp":420595200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[1983,5]]},"abstract":"<jats:p>Recurrence relations (RR) play an important role in many domains of Science. Mathematics, Physics or Computer Science are obvious examples. It is rather intriguing to remark that few attempts to handle them as generic objects have been made in the field of Computer Algebra [24]. The only genuine effort is due to Verbaeten [1] who studied recurrence relations of hypergeometric functions. The same type of functions was considered by Lafferty [2], who was interested in reducing them to elementary or special functions by doing pattern matching with RR.<\/jats:p>","DOI":"10.1145\/1089330.1089334","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"18-25","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Synthesizing recurrence relations I"],"prefix":"10.1145","volume":"17","author":[{"given":"Jacques","family":"Calmet","sequence":"first","affiliation":[{"name":"IMAG, Grenoble, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ian","family":"Cohen","sequence":"additional","affiliation":[{"name":"The Royal Institute of Technology, Stockholm, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[1983,5]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1086837.1086854"},{"key":"e_1_2_1_2_1","first-page":"465","volume-title":"Proceedings of the 1979 MACSYMA User's Conference","author":"Lafferty E. 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Burstall, \"Deriving Efficient Algorithms ..\", Acta Informatica 18, pp 181--206 (1982).","journal-title":"Acta Informatica"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/356827.356832"},{"key":"e_1_2_1_7_1","first-page":"1","volume-title":"in \"Theory and Applications of Special Functions\". Ed. R. A. Askey","author":"Gautschi W.","year":"1975","unstructured":"W. Gautschi , \"Computational Methods in Special Functions - A Survey\" , in \"Theory and Applications of Special Functions\". Ed. R. A. Askey , pp 1 -- 98 , Academic Press , N.Y. ( 1975 ). W. Gautschi, \"Computational Methods in Special Functions - A Survey\", in \"Theory and Applications of Special Functions\". Ed. R. A. Askey, pp 1--98, Academic Press, N.Y. (1975)."},{"key":"e_1_2_1_8_1","unstructured":"N. J. A. Sloane \"A Handbook of Integer Sequences\" Academic Press N.Y. (1973).  N. J. A. Sloane \"A Handbook of Integer Sequences\" Academic Press N.Y. (1973)."},{"key":"e_1_2_1_9_1","unstructured":"D. Jarden \"Recurring Sequences\" Riveon Lematematika Jerusalem (1966).  D. Jarden \"Recurring Sequences\" Riveon Lematematika Jerusalem (1966)."},{"key":"e_1_2_1_10_1","doi-asserted-by":"crossref","unstructured":"G. Szeg\u00f6 \"Orthogonal polynomials\" A.M.S. Colloquium Publication vol. 23 (1939).  G. Szeg\u00f6 \"Orthogonal polynomials\" A.M.S. Colloquium Publication vol. 23 (1939).","DOI":"10.1090\/coll\/023"},{"key":"e_1_2_1_11_1","unstructured":"L. Ya. Geronimus \"Orthogonal Polynomials\" Consultant Bureau N.Y. (1961).  L. Ya. Geronimus \"Orthogonal Polynomials\" Consultant Bureau N.Y. (1961)."},{"key":"e_1_2_1_12_1","volume-title":"Bateman Manuscript Project","author":"End\u00e9lyi A.","year":"1953","unstructured":"A. End\u00e9lyi , \" Higher Transcendental Functions \", Bateman Manuscript Project vol. I , II , McGraw- Hill, N.Y. ( 1953 ). A. End\u00e9lyi et al., \"Higher Transcendental Functions\", Bateman Manuscript Project vol. I, II, McGraw-Hill, N.Y. (1953)."},{"key":"e_1_2_1_13_1","volume-title":"Proceed. of Regional Conference Series in Applied Math. SIAM","author":"Askey R.","year":"1975","unstructured":"R. Askey , \"Orthogonal Polynomials and Special Functions\" , Proceed. of Regional Conference Series in Applied Math. SIAM ( 1975 ). R. Askey, \"Orthogonal Polynomials and Special Functions\", Proceed. of Regional Conference Series in Applied Math. SIAM (1975)."},{"key":"e_1_2_1_14_1","volume-title":"A Course of Modern Analysis","author":"Whittaker E. T.","year":"1952","unstructured":"E. T. Whittaker and G. N. Watson , \" A Course of Modern Analysis \", 4 th ed., Cambridge Univ. Press , Cambridge ( 1952 ). E. T. Whittaker and G. N. Watson, \"A Course of Modern Analysis\", 4th ed., Cambridge Univ. 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Buchholz, \"The Confluent Hypergeometric function\", Springer Trates in Natural Philosophy, vol. 15 (1969)."},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1949.11990232"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0065-2458(08)60033-9"},{"key":"e_1_2_1_22_1","volume-title":"Th\u00e8se 3i\u00e8me cycle","author":"Papon E.","year":"1981","unstructured":"E. Papon , \"Algoritmes de detection de relations de r\u00e9currences..\" , Th\u00e8se 3i\u00e8me cycle , Univ. Paris-Sud , Centre d'Orsay ( 1981 ) unpublished. E. Papon, \"Algoritmes de detection de relations de r\u00e9currences..\", Th\u00e8se 3i\u00e8me cycle, Univ. Paris-Sud, Centre d'Orsay (1981) unpublished."},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1089310.1089315"},{"volume-title":"B. Buchberger et.al.","author":"Loos R.","key":"e_1_2_1_24_1","unstructured":"R. Loos , Introduction to \"Computer Algebra \", Ed. B. 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