{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T04:20:50Z","timestamp":1775017250358,"version":"3.50.1"},"reference-count":29,"publisher":"Pleiades Publishing Ltd","issue":"2","license":[{"start":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T00:00:00Z","timestamp":1648771200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T00:00:00Z","timestamp":1648771200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Program Comput Soft"],"published-print":{"date-parts":[[2022,4]]},"DOI":"10.1134\/s0361768822020104","type":"journal-article","created":{"date-parts":[[2022,4,20]],"date-time":"2022-04-20T01:02:51Z","timestamp":1650416571000},"page":"125-146","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Symbolic Conversion of Holonomic Functions to Hypergeometric Type Power Series"],"prefix":"10.1134","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9199-7077","authenticated-orcid":false,"given":"Bertrand","family":"Teguia Tabuguia","sequence":"first","affiliation":[]},{"given":"Wolfram","family":"Koepf","sequence":"additional","affiliation":[]}],"member":"137","published-online":{"date-parts":[[2022,4,20]]},"reference":[{"key":"3660_CR1","doi-asserted-by":"crossref","unstructured":"Abramov, S.A., m-sparse solutions of linear ordinary differential equations with polynomial coefficients, Discrete Math., 2000, vol. 217, no. 1\u20133, pp. 3\u201315.","DOI":"10.1016\/S0012-365X(99)00252-6"},{"key":"3660_CR2","doi-asserted-by":"crossref","unstructured":"Abramov, S.A., Petkov\u0161ek, M., and Ryabenko, A., Special formal series solutions of linear operator equations, Discrete Math., 2000, vol. 210, no. 1\u20133, pp. 3\u201325.","DOI":"10.1016\/S0012-365X(99)00118-1"},{"key":"3660_CR3","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1016\/S0747-7171(08)80159-9","volume":"10","author":"G. Almkvist","year":"1990","unstructured":"Almkvist, G. and Zeilberger, D., The method of differentiating under the integral sign, J. Symb. Comput., 1990, vol. 10, no. 6, pp. 571\u2013592.","journal-title":"J. Symb. Comput."},{"key":"3660_CR4","unstructured":"Brewer, T., Algebraic properties of formal power series composition, Ph.D. Thesis, Univ. of Kentucky, 2014. https:\/\/uknowledge.uky.edu\/cgi\/viewcontent.cgi?article=1021&context=math_etds."},{"key":"3660_CR5","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/s00200-005-0192-x","volume":"17","author":"T. Cluzeau","year":"2006","unstructured":"Cluzeau, T. and van Hoeij, M., Computing hypergeometric solutions of linear recurrence equations, Appl. Algebra Eng. Comm. Comput., 2006, vol. 17, no. 2, pp.\u00a083\u2013115.","journal-title":"Appl. Algebra Eng. Comm. Comput."},{"key":"3660_CR6","first-page":"22","volume":"2","author":"D. Gruntz","year":"1995","unstructured":"Gruntz, D. and Koepf, W., Maple package on formal power series, Maple Tech. Newsl., 1995, vol. 2, no. 2, pp.\u00a022\u201328.","journal-title":"Maple Tech. Newsl."},{"key":"3660_CR7","doi-asserted-by":"crossref","unstructured":"Hendricks, P.A. and Singer, M.F., Solving difference equations in finite terms, J. Symb. Comput., 1999, vol.\u00a027, vol. 3, pp. 239\u2013259.","DOI":"10.1006\/jsco.1998.0251"},{"key":"3660_CR8","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/s11786-012-0107-8","volume":"6","author":"P. Horn","year":"2012","unstructured":"Horn, P., Koepf, W., and Sprenger, T., m-fold hypergeometric solutions of linear recurrence equations revisited, Math. Comput. Sci., 2012, vol. 6, no. 1, pp. 61\u201377.","journal-title":"Math. Comput. Sci."},{"key":"3660_CR9","volume-title":"The Concrete Tetrahedron. Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates","author":"M. Kauers","year":"2011","unstructured":"Kauers, M. and Paule, P., The Concrete Tetrahedron. Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates, Wien: Springer-Verlag, 2011."},{"key":"3660_CR10","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1016\/S0747-7171(10)80012-4","volume":"13","author":"W. Koepf","year":"1992","unstructured":"Koepf, W., Power series in computer algebra, J. Symb. Comput., 1992, vol. 13, no. 6, pp. 581\u2013603.","journal-title":"J. Symb. Comput."},{"key":"3660_CR11","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/s005910050032","volume":"44","author":"W. Koepf","year":"1997","unstructured":"Koepf, W., The algebra of holonomic equations, Math. Semesterber, 1997, vol. 44, pp. 173\u2013194.","journal-title":"Math. Semesterber"},{"key":"3660_CR12","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/S0377-0427(98)00023-5","volume":"90","author":"W. Koepf","year":"1998","unstructured":"Koepf, W. and Schmersau, D., Representations of orthogonal polynomials, J. Comput. Appl. Math., 1998, vol. 90, no. 1, pp. 57\u201394.","journal-title":"J. Comput. Appl. Math."},{"key":"3660_CR13","first-page":"321","volume":"94","author":"J. Lubin","year":"1994","unstructured":"Lubin, J., Nonarchimedean dynamical systems, Compos. Math., 1994, vol. 94, no. 3, pp. 321\u2013346.","journal-title":"Compos. Math."},{"key":"3660_CR14","unstructured":"Maplesoft, a. d. o. W. M. I., 2020. Maple 2021."},{"key":"3660_CR15","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/0747-7171(92)90038-6","volume":"14","author":"M. Petkov\u0161ek","year":"1992","unstructured":"Petkov\u0161ek, M., Hypergeometric solutions of linear recurrences with polynomial coefficients, J. Symb. Comput., 1992, vol. 14, no. 2-3, pp. 243\u2013264.","journal-title":"J. Symb. Comput."},{"key":"3660_CR16","series-title":"Finding all hypergeometric solutions of linear differential equations","volume-title":"ISSAC","author":"M. Petkov\u0161ek","year":"1993","unstructured":"Petkov\u0161ek, M. and Salvy, B., Finding all hypergeometric solutions of linear differential equations, in ISSAC, Bronstein, M., Ed., New York: Association for Computing Machinery, 1993, pp. 27\u201333."},{"key":"3660_CR17","series-title":"Special formal series solutions of linear ordinary differential equations","volume-title":"Formal Power Series and Algebraic Combinatorics","author":"A. Ryabenko","year":"2000","unstructured":"Ryabenko, A., Special formal series solutions of linear ordinary differential equations, in Formal Power Series and Algebraic Combinatorics, Springer, 2000, pp. 356\u2013366."},{"key":"3660_CR18","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1023\/A:1014880918779","volume":"28","author":"A.A. Ryabenko","year":"2002","unstructured":"Ryabenko, A.A., Formal solutions of linear ordinary differential equations containing m-hypergeometric series, Program. Comput. Software, 2002, vol. 28, no. 2, pp. 92\u2013101.","journal-title":"Program. Comput. Software"},{"key":"3660_CR19","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1145\/178365.178368","volume":"20","author":"B. Salvy","year":"1994","unstructured":"Salvy, B. and Zimmermann, P., Gfun: a maple package for the manipulation of generating and holonomic functions in one variable, ACM Trans. Math. Software, 1994, vol. 20, no. 2, pp. 163\u2013177.","journal-title":"ACM Trans. Math. Software"},{"key":"3660_CR20","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139058520","volume-title":"Enumerative Combinatorics","author":"R.P. Stanley","year":"2011","unstructured":"Stanley, R.P., Enumerative Combinatorics, 2nd ed., Cambridge, 2011, vol. 1."},{"key":"3660_CR21","unstructured":"Teguia Tabuguia, B., Power series representations of hypergeometric type and non-holonomic functions in computer algebra, Ph.D. Thesis, Univ. of Kassel, 2020. https:\/\/kobra.uni-kassel.de\/handle\/123456789\/11598."},{"key":"3660_CR22","unstructured":"Teguia Tabuguia, B., A variant of van Hoeij\u2019s algorithm to compute hypergeometric term solutions of holonomic recurrence equations, J. Algorithm Comput., 2021, vol. 53, no. 2, pp. 1\u201332."},{"key":"3660_CR23","unstructured":"Teguia Tabuguia, B. and Koepf, W., Hypergeometric type power series, in Proc. 4th Int. Conf. \u201cComputer Algebra\u201d, Abramov, S.A. and Sevastyanov, L.A., Eds., MAKS Press, 2021, vol. 28v pp. 105\u2013109."},{"key":"3660_CR24","series-title":"Power series representations of hypergeometric type functions","volume-title":"Maple in Mathematics Education and Research. MC 2020","author":"B. Teguia Tabuguia","year":"2021","unstructured":"Teguia Tabuguia, B. and Koepf, W., Power series representations of hypergeometric type functions, in Maple in Mathematics Education and Research. MC 2020, Corless, R., Gerhard, J., and Kotsireas, I., Eds., Springer, 2021, pp. 376\u2013393."},{"key":"3660_CR25","doi-asserted-by":"crossref","unstructured":"Van Hoeij, M., Finite singularities and hypergeometric solutions of linear recurrence equations, J. Pure Appl. Algebra, 1999, vol. 139, no. 1\u20133, pp. 109\u2013131.","DOI":"10.1016\/S0022-4049(99)00008-0"},{"key":"3660_CR26","unstructured":"Wolfram, S., The Mathematica Book, Version 4, 5th ed., Wolfram Media, Cambridge University Press, 2003."},{"key":"3660_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-29244-0","volume-title":"Commutative Algebra","author":"O. Zariski","year":"1960","unstructured":"Zariski, O. and Samuel, P., Commutative Algebra, New York: Springer-Verlag, 1960, Vol. 2."},{"key":"3660_CR28","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/0377-0427(90)90042-X","volume":"32","author":"D. Zeilberger","year":"1990","unstructured":"Zeilberger, D., A holonomic systems approach to special functions identities, J. Comput. Appl. Math., 1990, vol. 32, no. 3, pp. 321\u2013368.","journal-title":"J. Comput. Appl. Math."},{"key":"3660_CR29","doi-asserted-by":"crossref","unstructured":"Teguia Tabuguia, B. and Koepf, W., On the representation of non-holonomic power series, 2021. arXiv:2109.09574 [cs.SC].","DOI":"10.5206\/mt.v2i1.14315"}],"container-title":["Programming and Computer Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768822020104.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0361768822020104","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0361768822020104.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T02:43:36Z","timestamp":1775011416000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0361768822020104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4]]},"references-count":29,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["3660"],"URL":"https:\/\/doi.org\/10.1134\/s0361768822020104","relation":{},"ISSN":["0361-7688","1608-3261"],"issn-type":[{"value":"0361-7688","type":"print"},{"value":"1608-3261","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4]]},"assertion":[{"value":"8 August 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 September 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 September 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 April 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no conflicts of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"CONFLICT OF INTEREST"}}]}}