{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:18:07Z","timestamp":1776784687712,"version":"3.51.2"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"252","license":[{"start":{"date-parts":[[2006,3,15]],"date-time":"2006-03-15T00:00:00Z","timestamp":1142380800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Based on the Hadamard product of power series, polynomial series expansions for confluent hypergeometric functions\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper M left-parenthesis a comma c semicolon dot right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>M<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>c<\/mml:mi>\n                            <mml:mo>;<\/mml:mo>\n                            <mml:mo>\n                              \u22c5\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">M(a,c;\\cdot )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and for Gaussian hypergeometric functions\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper F left-parenthesis a comma b semicolon c semicolon dot right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>F<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>b<\/mml:mi>\n                            <mml:mo>;<\/mml:mo>\n                            <mml:mi>c<\/mml:mi>\n                            <mml:mo>;<\/mml:mo>\n                            <mml:mo>\n                              \u22c5\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">F(a,b;c;\\cdot )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    are introduced and studied. It turns out that the partial sums provide an interesting alternative for the numerical evaluation of the functions\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper M left-parenthesis a comma c semicolon dot right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>M<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>c<\/mml:mi>\n                            <mml:mo>;<\/mml:mo>\n                            <mml:mo>\n                              \u22c5\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">M(a,c;\\cdot )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper F left-parenthesis a comma b semicolon c semicolon dot right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>F<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>a<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>b<\/mml:mi>\n                            <mml:mo>;<\/mml:mo>\n                            <mml:mi>c<\/mml:mi>\n                            <mml:mo>;<\/mml:mo>\n                            <mml:mo>\n                              \u22c5\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">F(a,b;c;\\cdot )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , in particular, if the parameters are also viewed as variables.\n                  <\/p>","DOI":"10.1090\/s0025-5718-05-01734-5","type":"journal-article","created":{"date-parts":[[2005,8,10]],"date-time":"2005-08-10T10:23:21Z","timestamp":1123669401000},"page":"1937-1952","source":"Crossref","is-referenced-by-count":3,"title":["Polynomial series expansions for confluent and Gaussian hypergeometric functions"],"prefix":"10.1090","volume":"74","author":[{"given":"W.","family":"Luh","sequence":"first","affiliation":[]},{"given":"J.","family":"M\u00fcller","sequence":"additional","affiliation":[]},{"given":"S.","family":"Ponnusamy","sequence":"additional","affiliation":[]},{"given":"P.","family":"Vasundhra","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2005,3,15]]},"reference":[{"key":"1","series-title":"National Bureau of Standards Applied Mathematics Series, No. 55","volume-title":"Handbook of mathematical functions, with formulas, graphs and mathematical tables","year":"1966"},{"issue":"2","key":"2","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/S0377-0427(01)00417-4","article-title":"On hypergeometric functions and function spaces","volume":"139","author":"Balasubramanian, R.","year":"2002","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"key":"3","isbn-type":"print","volume-title":"Higher transcendental functions. Vol. I","author":"Erd\u00e9lyi, Arthur","year":"1981","ISBN":"https:\/\/id.crossref.org\/isbn\/089874069X"},{"issue":"1-2","key":"4","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1080\/17476939308814650","article-title":"On the Borel-Okada theorem and the Hadamard multiplication theorem","volume":"22","author":"Grosse-Erdmann, Karl-Goswin","year":"1993","journal-title":"Complex Variables Theory Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0278-1077","issn-type":"print"},{"key":"5","series-title":"Mathematics in Science and Engineering, Vol. 53","volume-title":"The special functions and their approximations, Vol. I","author":"Luke, Yudell L.","year":"1969"},{"key":"6","series-title":"Mathematics in Science and Engineering, Vol. 53","volume-title":"The special functions and their approximations. Vol. II","author":"Luke, Yudell L.","year":"1969"},{"issue":"3-4","key":"7","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1080\/17476939208814542","article-title":"The Hadamard multiplication theorem and applications in summability theory","volume":"18","author":"M\u00fcller, J\u00fcrgen","year":"1992","journal-title":"Complex Variables Theory Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0278-1077","issn-type":"print"},{"issue":"4","key":"8","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/s003659900120","article-title":"Convergence acceleration of Taylor sections by convolution","volume":"15","author":"M\u00fcller, J.","year":"1999","journal-title":"Constr. Approx.","ISSN":"https:\/\/id.crossref.org\/issn\/0176-4276","issn-type":"print"},{"key":"9","unstructured":"Ch. Schwarz, Computation of confluent hypergeometric functions and application to parabolic boundary control problems, Ph.D Thesis, University of Trier, 2001."},{"key":"10","isbn-type":"print","first-page":"357","article-title":"Computation and confluent hypergeometric functions on compact intervals","author":"Schwarz, Ch.","year":"2002","ISBN":"https:\/\/id.crossref.org\/isbn\/9639453005"},{"key":"11","series-title":"A Wiley-Interscience Publication","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032572","volume-title":"Special functions","author":"Temme, Nico M.","year":"1996","ISBN":"https:\/\/id.crossref.org\/isbn\/0471113131"},{"key":"12","series-title":"American Mathematical Society Colloquium Publications, Vol. XX","volume-title":"Interpolation and approximation by rational functions in the complex domain","author":"Walsh, J. L.","year":"1960","edition":"3"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2005-74-252\/S0025-5718-05-01734-5\/S0025-5718-05-01734-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-252\/S0025-5718-05-01734-5\/S0025-5718-05-01734-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:30:47Z","timestamp":1776781847000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-252\/S0025-5718-05-01734-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3,15]]},"references-count":12,"journal-issue":{"issue":"252","published-print":{"date-parts":[[2005,10]]}},"alternative-id":["S0025-5718-05-01734-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-05-01734-5","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2005,3,15]]}}}