{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T05:04:30Z","timestamp":1750309470168,"version":"3.41.0"},"reference-count":12,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2024,9,1]],"date-time":"2024-09-01T00:00:00Z","timestamp":1725148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p>We discuss principal branches for five square root functions and for the inverse trigonometric and inverse hyperbolic functions. We take the standard reference in this area to be the NIST Digital Library of Mathematical Functions (DLMF). We adopt the notation for and the definitions of the principal branches of the inverse functions in the DLMF. Similarly, the branch cuts for the inverse functions are defined as per the DLMF. Our goal is to use complex analysis to turn the definitions of the principal branches in the DLMF into concrete expressions that hold on the entirety of their respective cut planes. The square root principal branch expressions are new breakthrough discoveries that lead smoothly to four of the concrete expressions. We expand the number of concrete expressions in Sections 4.23 and 4.37 in the DLMF from two to eight. Three of these eight concrete expressions were in print in 1924. One of the latter is still awaiting inclusion in the DLMF. Taken altogether, we provide a computationally efficient resource for computer algebra in programming languages, specifically for the principal branches of the inverse trigonometric and inverse hyperbolic functions.<\/jats:p>","DOI":"10.1145\/3717582.3717583","type":"journal-article","created":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T20:41:51Z","timestamp":1739306511000},"page":"45-56","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Principal Branches of Inverse Trigonometric and Inverse Hyperbolic Functions"],"prefix":"10.1145","volume":"58","author":[{"given":"Kevin M.","family":"Dempsey","sequence":"first","affiliation":[{"name":"Wauwatosa, WI, USA"}]}],"member":"320","published-online":{"date-parts":[[2025,2,11]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"J. Napier. Mirifici Logarithmorum Canonis Descriptio [Description of the Wonderful Rule of Logarithms] 1614."},{"key":"e_1_2_1_2_1","volume-title":"US Government Printing Office","author":"Abramowitz M.","year":"1964","unstructured":"M. Abramowitz and I. A. Stegun, editors. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. US Government Printing Office, 1964."},{"issue":"7","key":"e_1_2_1_3_1","first-page":"585","article-title":"Irene Stegun, the Handbook of Mathematical Functions, and the Lingering Influence of the New Deal","volume":"113","author":"Grier D. A.","year":"2006","unstructured":"D. A. Grier. Irene Stegun, the Handbook of Mathematical Functions, and the Lingering Influence of the New Deal. Amer. Math. Monthly, 113(7):585--597, 2006.","journal-title":"Amer. Math. Monthly"},{"key":"e_1_2_1_4_1","first-page":"2024","article-title":"editors. NIST Digital Library of Mathematical Functions. https:\/\/dlmf.nist.gov\/","volume":"2","author":"Olver F. W. J.","unstructured":"F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders, H. S. Cohl, and M. A. McClain, editors. NIST Digital Library of Mathematical Functions. https:\/\/dlmf.nist.gov\/, Release 1.2.2 of 2024-09-15.","journal-title":"Release 1.2"},{"key":"e_1_2_1_5_1","unstructured":"E. W. Weisstein. Branch Cut From MathWorld-A Wolfram Web Resource. https:\/\/mathworld.wolfram.com\/BranchCut.html."},{"key":"e_1_2_1_6_1","volume-title":"Second Printing - Corrected.","author":"Johnson K. S.","year":"1925","unstructured":"K. S. Johnson. Transmission Circuits for Telephonic Communication: Methods of Analysis and Design, Second Printing - Corrected. New York: D. Van Nostrand Company, 1925."},{"key":"e_1_2_1_7_1","volume-title":"Tables of Integrals and Other Mathematical Data","author":"Dwight H. B.","year":"1961","unstructured":"H. B. Dwight. Tables of Integrals and Other Mathematical Data. 4th Ed., Macmillan Publishing Co., Inc., 1961.","edition":"4"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/362001.362023"},{"volume-title":"Wolfram Research","key":"e_1_2_1_9_1","unstructured":"Mathematica. Wolfram Research, Inc., Champaign, IL."},{"key":"e_1_2_1_10_1","unstructured":"Maple. Maplesoft a division of Waterloo Maple Inc. Waterloo Ontario."},{"key":"e_1_2_1_11_1","unstructured":"Wolfram Research. https:\/\/functions.wolfram.com\/ElementaryFunctions."},{"key":"e_1_2_1_12_1","volume-title":"Table of Integrals, Series, and Products: Corrected and Enlarged Edition","author":"Gradshteyn I. S.","year":"1980","unstructured":"I. S. Gradshteyn and I. M. Ryzhik. Table of Integrals, Series, and Products: Corrected and Enlarged Edition. Orlando, Florida: Academic Press, Inc., 1980."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3717582.3717583","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3717582.3717583","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:17:15Z","timestamp":1750295835000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3717582.3717583"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["10.1145\/3717582.3717583"],"URL":"https:\/\/doi.org\/10.1145\/3717582.3717583","relation":{},"ISSN":["1932-2232","1932-2240"],"issn-type":[{"type":"print","value":"1932-2232"},{"type":"electronic","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2024,9]]},"assertion":[{"value":"2025-02-11","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}