{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:05:05Z","timestamp":1776837905000,"version":"3.51.2"},"reference-count":6,"publisher":"American Mathematical Society (AMS)","issue":"347","license":[{"start":{"date-parts":[[2024,8,15]],"date-time":"2024-08-15T00:00:00Z","timestamp":1723680000000},"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 principal tool of computation used in this paper is classical Gaussian quadrature on the interval [0,1], which happens to be particularly effective here. Explicit expressions are found for the derivatives of the Ramanujan integral in question, and it is proved that the latter is completely monotone on\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis 0 comma normal infinity right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mn>0<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi mathvariant=\"normal\">\n                              \u221e\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(0,\\infty )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . As a byproduct, known series expansions for incomplete gamma functions are examined with regard to their convergence properties.\n                  <\/p>\n                  <p>The paper also pays attention to another famous integral, the Euler integral \u2014 better known as the gamma function \u2014 revitalizing a largely neglected part of the function, the part corresponding to negative values of the argument, which plays a prominent role in our work.<\/p>","DOI":"10.1090\/mcom\/3892","type":"journal-article","created":{"date-parts":[[2023,8,2]],"date-time":"2023-08-02T11:41:43Z","timestamp":1690976503000},"page":"1297-1308","source":"Crossref","is-referenced-by-count":2,"title":["A Ramanujan integral and its derivatives: computation and analysis"],"prefix":"10.1090","volume":"93","author":[{"given":"Walter","family":"Gautschi","sequence":"first","affiliation":[]},{"given":"Gradimir","family":"Milovanovi\u0107","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,8,15]]},"reference":[{"key":"1","first-page":"203","article-title":"The incomplete gamma functions since Tricomi","author":"Gautschi, Walter","year":"1998"},{"key":"2","unstructured":"G. H. Hardy, P. V. Seshu Alyar, and B. M. Wilson, eds., Collected Papers of Srinivasa Ramanujan, Cambridge University Press, Cambridge, 2015."},{"key":"3","unstructured":"A. B. Olde Daalhuis, Personal communication, November 3, 2022."},{"key":"4","unstructured":"A. B. Olde Daalhuis, Incomplete gamma and related functions, NIST Handbook of Mathematical Functions, National Institute of Standards and Technology and Cambridge University Press, 2010."},{"key":"5","isbn-type":"print","first-page":"321","article-title":"Confluent hypergeometric functions","author":"Olde Daalhuis, A. B.","year":"2010","ISBN":"https:\/\/id.crossref.org\/isbn\/9780521140638"},{"key":"6","doi-asserted-by":"crossref","unstructured":"Van E. Wood, Some integrals of Ramanujan and related contour integrals, Math. Comp. 20 (1966), 424\u2013429.","DOI":"10.1090\/S0025-5718-66-99927-3"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2024-93-347\/S0025-5718-2023-03892-3\/S0025-5718-2023-03892-3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:16:25Z","timestamp":1776834985000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2024-93-347\/S0025-5718-2023-03892-3\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,15]]},"references-count":6,"journal-issue":{"issue":"347","published-print":{"date-parts":[[2024,5]]}},"alternative-id":["S0025-5718-2023-03892-3"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3892","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":[[2023,8,15]]}}}