{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T17:03:11Z","timestamp":1784134991562,"version":"3.55.0"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"307","license":[{"start":{"date-parts":[[2018,3,3]],"date-time":"2018-03-03T00:00:00Z","timestamp":1520035200000},"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 evaluate each Stieltjes constant\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"gamma Subscript m\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>\n                              \u03b3\n                              \n                            <\/mml:mi>\n                            <mml:mi>m<\/mml:mi>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\gamma _m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    as a finite sum involving the first\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"m plus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>m<\/mml:mi>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">m+1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    Bernoulli numbers\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper B Subscript k\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>B<\/mml:mi>\n                            <mml:mi>k<\/mml:mi>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">B_k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and the first\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"m plus 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>m<\/mml:mi>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">m+1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    derivatives\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis negative 1 right-parenthesis Superscript k Baseline alpha Subscript k\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:msup>\n                              <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <mml:mi>k<\/mml:mi>\n                            <\/mml:msup>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03b1\n                                \n                              <\/mml:mi>\n                              <mml:mi>k<\/mml:mi>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(-1)^k\\alpha _k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of the alternating zeta function at the point 1. In turn, we compute each\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"alpha Subscript k\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>\n                              \u03b1\n                              \n                            <\/mml:mi>\n                            <mml:mi>k<\/mml:mi>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\alpha _k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in an efficient way by means of a series with geometric rate 1\/3. The coefficients of such a series are bounded and slowly decrease to zero. The computational significance of the preceding results is also discussed.\n                  <\/p>","DOI":"10.1090\/mcom\/3176","type":"journal-article","created":{"date-parts":[[2016,5,26]],"date-time":"2016-05-26T08:34:48Z","timestamp":1464251688000},"page":"2479-2492","source":"Crossref","is-referenced-by-count":10,"title":["Fast computation of the Stieltjes constants"],"prefix":"10.1090","volume":"86","author":[{"given":"Jos\u00e9","family":"Adell","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alberto","family":"Lekuona","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2017,3,3]]},"reference":[{"issue":"2128","key":"1","doi-asserted-by":"publisher","first-page":"954","DOI":"10.1098\/rspa.2010.0397","article-title":"Asymptotic estimates for Stieltjes constants: a probabilistic approach","volume":"467","author":"Adell, Jos\u00e9 A.","year":"2011","journal-title":"Proc. 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