{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T01:44:10Z","timestamp":1784339050636,"version":"3.55.0"},"reference-count":35,"publisher":"American Mathematical Society (AMS)","issue":"276","license":[{"start":{"date-parts":[[2012,3,2]],"date-time":"2012-03-02T00:00:00Z","timestamp":1330646400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The modified Abel lemma on summation by parts is employed to investigate the partial sum of Dougall\u2019s bilateral\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"Subscript 2 Baseline upper H 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi\/>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:msub>\n                              <mml:mi>H<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">_2H_2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -series. Several unusual transformations into fast convergent series are established. They lead surprisingly to numerous infinite series expressions for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"pi\">\n                        <mml:semantics>\n                          <mml:mi>\n                            \u03c0\n                            \n                          <\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">\\pi<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , including several formulae discovered by Ramanujan\u00a0(1914) and recently by Guillera\u00a0(2008).\n                  <\/p>","DOI":"10.1090\/s0025-5718-2011-02474-9","type":"journal-article","created":{"date-parts":[[2011,3,2]],"date-time":"2011-03-02T11:29:05Z","timestamp":1299065345000},"page":"2223-2251","source":"Crossref","is-referenced-by-count":32,"title":["Dougall\u2019s bilateral \u2082\ud835\udc3b\u2082-series and Ramanujan-like \ud835\udf0b-formulae"],"prefix":"10.1090","volume":"80","author":[{"given":"Wenchang","family":"Chu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2011,3,2]]},"reference":[{"issue":"9","key":"1","doi-asserted-by":"publisher","first-page":"852","DOI":"10.2307\/2975292","article-title":"A simple formula for \ud835\udf0b","volume":"104","author":"Adamchik, Victor","year":"1997","journal-title":"Amer. 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