{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:41:31Z","timestamp":1776836491075,"version":"3.51.2"},"reference-count":10,"publisher":"American Mathematical Society (AMS)","issue":"250","license":[{"start":{"date-parts":[[2005,11,2]],"date-time":"2005-11-02T00:00:00Z","timestamp":1130889600000},"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                    We present a numerical method for approximating an indefinite integral by the double exponential sinc method. The approximation error of the proposed method with\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N\">\n                        <mml:semantics>\n                          <mml:mi>N<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">N<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    integrand function evaluations is\n                    <disp-formula content-type=\"math\/mathml\">\n                      \\[\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper O left-parenthesis exp left-parenthesis minus c 1 upper N slash log left-parenthesis c 2 upper N right-parenthesis right-parenthesis right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"normal\">O<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>exp<\/mml:mi>\n                            <mml:mo>\n                              \u2061\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>c<\/mml:mi>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mi>log<\/mml:mi>\n                            <mml:mo>\n                              \u2061\n                              \n                            <\/mml:mo>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>c<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathrm {O}(\\exp (-c_1 N\/\\log (c_2 N)))<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                      \\]\n                    <\/disp-formula>\n                    for a reasonably wide class of integrands, including those with endpoint singularities. The proposed method compares favorably with the existing formulas based on the ordinary sinc method. Computational results show the accordance of the actual convergence rates with the theoretical estimate.\n                  <\/p>","DOI":"10.1090\/s0025-5718-04-01724-7","type":"journal-article","created":{"date-parts":[[2005,1,14]],"date-time":"2005-01-14T14:25:09Z","timestamp":1105712709000},"page":"655-679","source":"Crossref","is-referenced-by-count":9,"title":["Numerical indefinite integration by double exponential sinc method"],"prefix":"10.1090","volume":"74","author":[{"given":"Ken\u2019ichiro","family":"Tanaka","sequence":"first","affiliation":[]},{"given":"Masaaki","family":"Sugihara","sequence":"additional","affiliation":[]},{"given":"Kazuo","family":"Murota","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2004,11,2]]},"reference":[{"key":"1","volume-title":"Entire functions","author":"Boas, Ralph Philip, Jr.","year":"1954"},{"issue":"201","key":"2","doi-asserted-by":"publisher","first-page":"279","DOI":"10.2307\/2153166","article-title":"Two formulas for numerical indefinite integration","volume":"60","author":"Haber, Seymour","year":"1993","journal-title":"Math. 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Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"issue":"3","key":"8","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s002110050244","article-title":"Optimality of the double exponential formula\u2014functional analysis approach","volume":"75","author":"Sugihara, Masaaki","year":"1997","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"242","key":"9","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1090\/S0025-5718-02-01451-5","article-title":"Near optimality of the sinc approximation","volume":"72","author":"Sugihara, Masaaki","year":"2003","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"10","doi-asserted-by":"publisher","first-page":"721","DOI":"10.2977\/prims\/1195192451","article-title":"Double exponential formulas for numerical integration","volume":"9","author":"Takahasi, Hidetosi","year":"1973","journal-title":"Publ. Res. Inst. Math. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0034-5318","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2005-74-250\/S0025-5718-04-01724-7\/S0025-5718-04-01724-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-250\/S0025-5718-04-01724-7\/S0025-5718-04-01724-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:04:20Z","timestamp":1776780260000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-250\/S0025-5718-04-01724-7\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,11,2]]},"references-count":10,"journal-issue":{"issue":"250","published-print":{"date-parts":[[2005,4]]}},"alternative-id":["S0025-5718-04-01724-7"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-04-01724-7","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":[[2004,11,2]]}}}