Editing Gudermannian function (section)

== References ==
{{sfn whitelist |CITEREFRoyOlver2010}}
{{refbegin|30em}}
* {{cite journal |last=
  Barnett |first=Janet Heine |author-link=Janet Barnett |year=
  2004 |title=Enter, Stage Center: The Early Drama of the Hyperbolic Functions |journal=Mathematics Magazine |volume=77 |issue=1 |pages=15–30 |doi=10.1080/0025570X.2004.11953223 |url=https://www.maa.org/sites/default/files/321922717729.pdf.bannered.pdf }}
* {{cite book |last1=
  Becker |first1=George Ferdinand |author-link1=George Ferdinand Becker |last2=
  Van Orstrand |first2=Charles Edwin |year=
  1909 |title=Hyperbolic Functions |series=Smithsonian Mathematical Tables |publisher=Smithsonian Institution |url=https://archive.org/details/smithsonianmathe00smituoft}}
* {{cite journal |last=
  Becker |first=George Ferdinand |year=
  1912 |title=The gudermannian complement and imaginary geometry |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |volume=24 |issue=142 |pages=600–608 |doi=10.1080/14786441008637363 |url=https://ia600708.us.archive.org/view_archive.php?archive=/28/items/crossref-pre-1923-scholarly-works/10.1080%252F14786440908635958.zip&file=10.1080%252F14786441008637363.pdf }}
* {{cite book |editor-last=
  Beyer |editor-first=William H. |year=
  1987 |title=CRC Handbook of Mathematical Sciences |edition=6th |pages=268–286 |publisher=CRC Press |url=https://archive.org/details/crchandbookofmat00beye/ |url-access=limited }}
* {{cite journal |last=
  Cayley |first=Arthur |author-link=Arthur Cayley |year=
  1862 |title=On the transcendent <math display=inline>\operatorname{gd} u = \tfrac{1}{i}\log \tan \bigl(\tfrac14\pi + \tfrac12 ui\bigr)</math> |journal=Philosophical Magazine |series=4th Series |volume=24 |issue=158 |pages=19–21 |url=https://archive.org/details/londonedinburg4241862lond/page/19 |doi=10.1080/14786446208643307 }}
* {{cite journal |last1=
  Good |first1=Michael R.R. |last2=
  Anderson |first2=Paul R. |last3=
  Evans |first3=Charles R. |year=
  2013 |title=Time dependence of particle creation from accelerating mirrors |journal=Physical Review D |volume=88 |issue=2 |pages=025023 |arxiv=1303.6756  |doi=10.1103/PhysRevD.88.025023 }}
* {{cite web |last=
  Gottschalk |first=Walter |author-link=Walter_Gottschalk |year=
  2003 |title=Good Things about the Gudermannian |website=Gottschalk's Gestalts |url=https://gottschalksgestalts.org/pdf/GG88.pdf}}
* {{cite book |last=
  Gudermann |first=Christoph |author-link=Christoph Gudermann |year=
  1833 |title=Theorie der Potenzial- oder cyklisch-hyperbolischen Functionen |publisher=G. Reimer |language=de |trans-title=Theory of Potential- or Circular-Hyperbolic Functions |url=https://archive.org/details/theoriederpotenz00gude }}
* {{cite arXiv |last1=
  Jennings |first1=George |last2=
  Ni |first2= David |last3=
  Pong |first3=Wai Yan |last4=
  Raianu |first4=Serban |year=
  2022 |title=The Integral of Secant and Stereographic Projections of Conic Sections |class=math.HO |eprint = 2204.11187  }}
* {{cite tech report |last1=
  Kahlig |first1=Peter |last2=
  Reich |first2=Ludwig |year=
  2013 |title=Contributions to the theory of the Legendre-Gudermann equation |publisher=Fachbibliothek für Mathematik, Karl-Franzens-Universität Graz |url=https://www.researchgate.net/profile/Peter-Kahlig/publication/263491672_Contributions_to_the_theory_of_the_Legendre-Gudermann_equation/links/53e4d6930cf25d674e94f819/Contributions-to-the-theory-of-the-Legendre-Gudermann-equation.pdf }}
* {{cite journal |last=
  Karney |first=Charles F.F. |year=
  2011 |title=Transverse Mercator with an accuracy of a few nanometers |journal=Journal of Geodesy |volume=85 |issue=8 |pages=475–485 |arxiv=1002.1417 |doi=10.1007/s00190-011-0445-3 |url=https://geographiclib.sourceforge.io/tm.html }}
* {{cite journal |last=
  Kennelly |first=Arthur E. |year=
  1928 |title=Gudermannian Complex Angles |journal=Proceedings of the National Academy of Sciences |volume=14 |number=11 |pages=839–844 |doi=10.1073/pnas.14.11.839 |doi-access=free |pmc=1085762 }}
* {{cite journal |last=
  Kennelly |first=Arthur E. |year=
  1929 |title=Gudermannians and Lambertians with Their Respective Addition Theorems |journal=Proceedings of the American Philosophical Society |volume=68 |issue=3 |pages=175–184 |url=https://archive.org/details/dli.ministry.19102/page/175 }}
* {{cite journal |last=
  Lambert |first=Johann Heinrich |author-link=Johann Heinrich Lambert |year=
  1761 |publication-date=1768 |title=Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques |language=fr |trans-title=Memoir on some remarkable properties of the circular and logarithmic transcendental quantities |journal=Histoire de l'Académie Royale des Sciences et des Belles-Lettres |publication-place=Berlin |volume=17 |pages=265–322 |url=https://babel.hathitrust.org/cgi/pt?id=nyp.33433009864251&view=1up&seq=301&skin=2021 }}
* {{cite book |last=
  Lee |first=Laurence Patrick |author-link = Laurence Patrick Lee |year=
  1976 |title=Conformal Projections Based on Elliptic Functions |location=Toronto |publisher=B. V. Gutsell, York University |series=''Cartographica Monographs'' |volume=16 |url=https://archive.org/details/conformalproject0000leel |url-access=limited |isbn=0-919870-16-3 }} Supplement No. 1 to [https://www.utpjournals.press/toc/cart/13/1 ''The Canadian Cartographer'' '''13'''].
* {{cite book |last=
  Legendre |first=Adrien-Marie |author-link=Adrien-Marie Legendre |year=
  1817 |title=Exercices de calcul intégral |volume=2 |trans-title=Exercises in integral calculus |language=fr |publisher=Courcier |url=https://archive.org/details/exercicescalculi02legerich }}
* {{cite journal |last=
  Majernik |first=V. |year=
  1986 |title=Representation of relativistic quantities by trigonometric functions |journal=American Journal of Physics |volume=54 |issue=6 |pages=536–538 |url=https://www.researchgate.net/publication/252401386 |doi=10.1119/1.14557 }}
* {{cite book |last=
  McMahon |first=James |author-link=James McMahon (mathematician) |year=
  1906 |title=Hyperbolic Functions |publisher=Wiley |url=https://archive.org/details/hyperbolicfuncti00mcmauoft}} [First published as {{cite book |last=McMahon |editor1-last=Merriman |editor2-last=Woodward |year=1896 |publisher=Wiley |chapter=IV. Hyperbolic Functions |title=Higher Mathematics |chapter-url=https://archive.org/details/highermathematic00merrrich/page/107 |pages=107–168 }}]
* {{cite web |last=
  Masson |first=Paul |title=The Complex Gudermannian |year=
  2021 |url=https://analyticphysics.com/Complex%20Variables/The%20Complex%20Gudermannian%20Function.htm |website=Analytic Physics}}
* {{cite web |last=
  Osborne |first=Peter |year=
  2013  |title=The Mercator projections |url=https://ccv.eng.wayne.edu/reference/mercator-15dec2015.pdf }}
* {{cite journal |last=
  Peters |first=J. M. H. |year=
  1984 |title=The Gudermannian |journal=The Mathematical Gazette |volume=68 |issue=445 |pages=192–196 |doi=10.2307/3616342 |jstor=3616342 }}
* {{cite journal |last=
  Reynolds |first=William F. |year=
  1993 |title=Hyperbolic Geometry on a Hyperboloid |journal=The American Mathematical Monthly |volume=100 |issue=5 |pages=442–455 |doi=10.1080/00029890.1993.11990430 |url=http://people.ucsc.edu:80/~rmont/classes/ClassicalGeometry/web2016/sources/Hyperbolic_AmerMathMonthly.pdf |archive-url=https://web.archive.org/web/20160528134406id_/http://people.ucsc.edu:80/~rmont/classes/ClassicalGeometry/web2016/sources/Hyperbolic_AmerMathMonthly.pdf |archive-date=2016-05-28 |url-status=dead }}
* {{cite journal |last1=
  Rickey |first1=V. Frederick |last2=
  Tuchinsky |first2=Philip M. |year=
  1980 |title=An application of geography to mathematics: History of the integral of the secant |journal=Mathematics Magazine |volume=53 |issue=3 |pages=162–166 |doi=10.1080/0025570X.1980.11976846 |url=https://www.maa.org/sites/default/files/0025570x15087.di021115.02p0115x.pdf }}
* {{cite journal |last1=
  Ringermacher |first1=Harry I. |last2=
  Mead |first2=Lawrence R. |year=
  2009 |title=A new formula describing the scaffold structure of spiral galaxies |journal=Monthly Notices of the Royal Astronomical Society |volume=397 |issue=1 |pages=164–171 |doi=10.1111/j.1365-2966.2009.14950.x |doi-access=free |arxiv=0908.0892 }}
* {{cite journal |last=
  Robertson |first=John S. |year=
  1997 |title=Gudermann and the simple pendulum |journal=The College Mathematics Journal |volume=28 |issue=4 |pages=271–276 |doi=10.2307/2687148 |jstor=2687148 }}
* {{cite journal |last=
  Romakina |first=Lyudmila N. |year=
  2018 |title=The inverse Gudermannian in the hyperbolic geometry |journal=Integral Transforms and Special Functions |volume=29 |issue=5 |pages=384–401 |doi=10.1080/10652469.2018.1441296 |url=https://www.researchgate.net/publication/320517449 }}
* {{dlmf |last1=
  Roy |first1=Ranjan |last2=
  Olver |first2=Frank W. J. |author-link2=Frank W. J. Olver |id=4 |title=4. Elementary Functions |display-editors=1 }}
* {{cite journal |last=
  Sala |first=Kenneth L. |year=
  1989 |title=Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean |journal=SIAM Journal on Mathematical Analysis |volume=20 |issue=6 |pages=1514–1528 |url=http://kensala.com/publications/Sala_TransformationsOfTheJacobianAmplitudeFunctionAndItsCalculationViaTheArithmeticGeometricMean_SiamJMathsAnalysis_20_1989.pdf |doi=10.1137/0520100 }}
{{refend}}