Editing Exponentiation (section)

==References==
{{Reflist|refs=
<ref name="Backus_1954">{{cite book |title=Specifications for: The IBM Mathematical FORmula TRANSlating System, FORTRAN |type=Preliminary report |author-last1=Backus |author-first1=John Warner |author-link1=John Warner Backus |author-last2=Herrick |author-first2=Harlan L. |author-last3=Nelson |author-first3=Robert A. |author-last4=Ziller |author-first4=Irving |editor-last=Backus |editor-first=John Warner |editor-link=John Warner Backus |publisher=Programming Research Group, Applied Science Division, [[International Business Machines Corporation]] |location=New York, USA |date=1954-11-10 |pages=4, 6 |url=https://archive.computerhistory.org/resources/text/Fortran/102679231.05.01.acc.pdf |access-date=2022-07-04 |url-status=live |archive-url=https://web.archive.org/web/20220329234459/https://archive.computerhistory.org/resources/text/Fortran/102679231.05.01.acc.pdf |archive-date=2022-03-29}} (29 pages)</ref>
<ref name="Sayre_1956">{{cite book |title=The FORTRAN Automatic Coding System for the IBM 704 EDPM: Programmer's Reference Manual |publisher=Applied Science Division and Programming Research Department, [[International Business Machines Corporation]] |location=New York, USA |date=1956-10-15 |editor-last=Sayre |editor-first=David |editor-link=David Sayre |author-last1=Backus |author-first1=John Warner |author-link1=John Warner Backus |author-last2=Beeber |author-first2=R. J. |author-last3=Best |author-first3=Sheldon F. |author-last4=Goldberg |author-first4=Richard |author-link4=Richard Goldberg |author-last5=Herrick |author-first5=Harlan L. |author-last6=Hughes |author-first6=R. A. |author-last7=Mitchell |author-first7=L. B. |author-last8=Nelson |author-first8=Robert A. |author-last9=Nutt |author-first9=Roy |author-link9=Roy Nutt |author-first10=David |author-last10=Sayre |author-link10=David Sayre |author-first11=Peter B. |author-last11=Sheridan |author-first12=Harold |author-last12=Stern |author-first13=Irving |author-last13=Ziller |page=15 |url=https://archive.computerhistory.org/resources/text/Fortran/102649787.05.01.acc.pdf |access-date=2022-07-04 |url-status=live |archive-url=https://web.archive.org/web/20220704193549/http://archive.computerhistory.org/resources/text/Fortran/102649787.05.01.acc.pdf |archive-date=2022-07-04}} (2+51+1 pages)</ref>
<ref name="Bronstein_1987">{{cite book |title=Taschenbuch der Mathematik |language=de |trans-title=Pocketbook of mathematics |title-link=Bronstein and Semendjajew |chapter=2.4.1.1. Definition arithmetischer Ausdrücke |trans-chapter=Definition of arithmetic expressions |author-last1=Bronstein |author-first1=Ilja Nikolaevič<!-- Nikolajewitsch --> |author-link1=Ilya Nikolaevich Bronshtein<!-- 1903–1976 --> |author-last2=Semendjajew |author-first2=Konstantin Adolfovič<!-- Adolfowitsch --> |author-link2=Konstantin Adolfovic Semendyayev<!-- 1908–1988 --> |editor-first1=Günter |editor-last1=Grosche |editor-first2=Viktor |editor-last2=Ziegler<!-- 1922–1980--> |editor-first3=Dorothea |editor-last3=Ziegler |others=Weiß, Jürgen<!-- lector --> |translator-last=Ziegler |translator-first=Viktor |volume=1 |date=1987 |edition=23 |orig-year=1945 |publisher=[[Verlag Harri Deutsch]] (and [[B. G. Teubner Verlagsgesellschaft]], Leipzig) |publication-place=Thun, Switzerland / Frankfurt am Main, Germany |location=Leipzig, Germany |isbn=3-87144-492-8 |pages=115–120, 802 <!-- |quote=Regel 7: Ist ''F''(''A'') Teilzeichenreihe eines arithmetischen Ausdrucks oder einer seiner Abkürzungen und ''F'' eine Funktionenkonstante und ''A'' eine Zahlenvariable oder Zahlenkonstante, so darf ''F{{thin space}}A'' dafür geschrieben werden. [Darüber hinaus ist noch die Abkürzung ''F''<sup>''n''</sup>(''A'') für (''F''(''A''))<sup>''n''</sup> üblich. Dabei kann ''F'' sowohl Funktionenkonstante als auch Funktionenvariable sein.] -->}}</ref>
<ref name="NIST_2010">{{cite book |title=NIST Handbook of Mathematical Functions |title-link=NIST Handbook of Mathematical Functions |editor-last=Olver |editor-first=Frank W. J. |editor2-last=Lozier |editor2-first=Daniel W. |editor3-last=Boisvert |editor3-first=Ronald F. |editor4-last=Clark |editor4-first=Charles W. |date=2010 |publisher=[[National Institute of Standards and Technology]] (NIST), [[U.S. Department of Commerce]], [[Cambridge University Press]] |isbn=978-0-521-19225-5 |mr=2723248}}[http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521140638]</ref>
<ref name="Zeidler_2013">{{cite book |title=Springer-Handbuch der Mathematik I |title-link=Springer-Handbuch der Mathematik |volume=I |language=de |editor-last=Zeidler |editor-first=Eberhard |editor-link=:de:Eberhard Zeidler |author-last1=Zeidler |author-first1=Eberhard |author-link1=:de:Eberhard Zeidler |author-last2=Schwarz |author-first2=Hans Rudolf |author-last3=Hackbusch |author-first3=Wolfgang |author-link3=Wolfgang Hackbusch |author-last4=Luderer |author-first4=Bernd |author-link4=:de:Bernd Luderer |author-last5=Blath |author-first5=Jochen |author-last6=Schied |author-first6=Alexander |author-last7=Dempe |author-first7=Stephan |author-last8=Wanka |author-first8=Gert |author-link8=Gert Wanka |author-last9=Hromkovič |author-first9=Juraj |author-link9=Juraj Hromkovič |author-last10=Gottwald |author-first10=Siegfried |author-link10=Siegfried Gottwald |publisher=[[Springer Spektrum]], [[Springer Fachmedien Wiesbaden]] |location=Berlin / Heidelberg, Germany |edition=1 |date=2013 |orig-year=2012 |isbn=978-3-658-00284-8 |page=590<!-- |doi=10.1007/978-3-658-00285-5 |url=https://link.springer.com/book/10.1007/978-3-658-00285-5 |access-date=2024-01-11 -->}} (xii+635 pages)</ref>
<!-- <ref name="Stibitz_1957">{{cite book |title=Mathematics and Computers |author-last1=Stibitz |author-first1=George Robert |author-link1=George Robert Stibitz |author-last2=Larrivee |author-first2=Jules A. |date=1957 |edition=1 |publisher=[[McGraw-Hill Book Company, Inc.]] |publication-place=New York, USA / Toronto, Canada / London, UK |location=Underhill, Vermont, USA |lccn=56-10331 |page=169}} (10+228 pages) (NB. Stibitz uses parentheses even in conjunction with trigonometric functions (like <code>(cos&nbsp;''u'')<sup>''n''</sup></code>) to avoid the ambiguity of the <code>cos<sup>''n''</sup>&nbsp;''u''</code> notation.)</ref> -->
<ref name="Cajori_1929">{{cite book |author-last=Cajori |author-first=Florian |author-link=Florian Cajori |title=A History of Mathematical Notations |volume=2 |orig-year=March 1929 |publisher=[[Open court publishing company]] |location=Chicago, USA |date=1952 |edition=3rd |pages=108, 176–179, 336, 346 |isbn=978-1-60206-714-1 |url=https://books.google.com/books?id=bT5suOONXlgC |access-date=2016-01-18}}</ref>
<!-- <ref name="Peirce_1852">{{cite book |author-last=Peirce |author-first=Benjamin |author-link=Benjamin Peirce |title=Curves, Functions and Forces |volume=I |edition=new |location=Boston, USA |date=1852 |page=203}}</ref>-->
<ref name="Peano_1903">{{cite book |author-last=Peano |author-first=Giuseppe |author-link=Giuseppe Peano |title=Formulaire mathématique |language=fr |volume=IV |date=1903 |page=229}}</ref>
<!-- <ref name="Pringsheim-Molk_1907">{{cite book |author-last1=Pringsheim |author-first1=Alfred |author-link1=Alfred Pringsheim |author-last2=Molk |author-first2=Jules |author-link2=Jules Molk |title=Encyclopédie des sciences mathématiques pures et appliquées |language=fr |id=Part I |volume=I |date=1907 |page=195}}</ref> -->
<ref name="Herschel_1813">{{cite journal |author-last=Herschel |author-first=John Frederick William |author-link=John Frederick William Herschel |title=On a Remarkable Application of Cotes's Theorem |journal=[[Philosophical Transactions of the Royal Society of London]] |publisher=[[Royal Society of London]], printed by W. Bulmer and Co., Cleveland-Row, St. James's, sold by G. and W. Nicol, Pall-Mall |location=London |volume=103 |number=Part 1 |date=1813 |orig-year=1812-11-12 |jstor=107384 |pages=8–26 [10] |s2cid=118124706 |doi=10.1098/rstl.1813.0005}}</ref>
<ref name="Herschel_1820">{{cite book |author-last=Herschel |author-first=John Frederick William |author-link=John Frederick William Herschel |title=A Collection of Examples of the Applications of the Calculus of Finite Differences |chapter=Part III. Section I. Examples of the Direct Method of Differences |location=Cambridge, UK |publisher=Printed by J. Smith, sold by J. Deighton & sons |date=1820 |pages=1–13 [5–6] |chapter-url=https://books.google.com/books?id=PWcSAAAAIAAJ&pg=PA5 |access-date=2020-08-04 |url-status=live |archive-url=https://web.archive.org/web/20200804031020/https://books.google.de/books?id=PWcSAAAAIAAJ&jtp=5 |archive-date=2020-08-04}} [https://archive.org/details/acollectionexam00lacrgoog] (NB. Inhere, Herschel refers to his {{citeref|Herschel|1813|1813 work|style=plain}} and mentions [[Hans Heinrich Bürmann]]'s older work.)</ref>
<ref name="Euler_1748">{{cite book |author-last=Euler |author-first=Leonhard |author-link=Leonhard Euler |title=Introductio in analysin infinitorum |language=la |location=Lausanne |publisher=Marc-Michel Bousquet |date=1748 |volume=I |pages=69, 98–99 <!-- |quote-page=69 --> |url=https://gallica.bnf.fr/ark:/12148/bpt6k33510/f93.image |quote=Primum ergo considerandæ sunt quantitates exponentiales, seu Potestates, quarum Exponens ipse est quantitas variabilis. Perspicuum enim est hujusmodi quantitates ad Functiones algebraicas referri non posse, cum in his Exponentes non nisi constantes locum habeant.}}</ref>
<!-- <ref name="Euler_1760">{{cite journal |author-last=Euler |author-first=Leonhard |author-link=Leonhard Euler |title=Novi commentarii Academiae Scientiarum Imperialis Petropolitanae, for the years 1754–1755 |language=la |location=Petropoli |date=1760 |orig-year=1754 |page=172}}</ref> -->
<!-- <ref name="Karsten_1760">{{cite book |author-last=Karsten |author-first=Wenceslaus Johann Gustav |author-link=Wenceslaus Johann Gustav Karsten |title=Mathesis theoretica Elementaris Atque Sublimior |language=la |chapter=Sectio XIII. De sectionibus angulorum et arcuum circularium |location=Rostock |date=1760 |page=511 |url=https://www.digitale-sammlungen.de/de/view/bsb10594020?page=539 |access-date=2020-08-04}} [http://mdz-nbn-resolving.de/urn:nbn:de:bvb:12-bsb10594020-6 ]</ref> -->
<!-- <ref name="Scherffer_1772">{{cite book |author-last=Scherffer |author-first=Karl "Carolo" |author-link=:d:Q55072319 |title=Institutionum analyticarum, pars secunda |language=la |location=Vienna |date=1772 |page=144}}</ref> -->
<!-- <ref name="Frisius_1782">{{cite book |author-last=Frisius (Frisii) |author-first=Paulli |author-link=:s:de:BLKÖ:Frisi,_Paul |title=Operum tomus primus |language=la |location=Milano |date=1782 |page=303}}</ref> -->
<!-- <ref name="Abel_1826">{{cite journal |author-last=Abel |author-first=Niels Henrik |author-link=Niels Henrik Abel |language=de |journal=[[Journal für die reine und angewandte Mathematik]] |publisher=[[August Leopold Crelle]] |volume=I |location=Berlin |date=1826 |pages=318–337 |postscript=;}} {{cite journal |author-last=Abel |author-first=Niels Henrik |author-link=Niels Henrik Abel |language=de |journal=[[Journal für die reine und angewandte Mathematik]] |publisher=[[August Leopold Crelle]] |volume=II |location=Berlin |date=1827 |page=26}}</ref> -->
<!-- <ref name="Ohm_1829">{{cite book |author-last=Ohm |author-first=Martin |author-link=Martin Ohm |title=System der Mathematik |language=de |id=Part 3 |location=Berlin |date=1829 |page=21}}</ref> -->
<!-- <ref name="Cagnoli_1786">{{cite book |author-last=Cagnoli |author-first=Antonio |author-link=Antonio Cagnoli |title=Traité de Trigonométrie |language=fr |publisher=trad. par Chompré |location=Paris |date=1786 |page=20}}</ref> -->
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<!-- <ref name="Serret_1857">{{cite book |author-last=Serret |author-first=Joseph Alfred |author-link=Joseph Alfred Serret |title=Traité de Trigonométrie |language=fr |edition=2nd |location=Paris |date=1857 |page=12}}</ref> -->
<!-- <ref name="Todhunter_1876">{{cite book |author-last=Todhunter |author-first=Isaac |author-link=Isaac Todhunter |title=Plane Trigonometry |edition=6th |location=London |date=1876 |page=19}}</ref> -->
<!-- <ref name="Hobson_1911">{{cite book |author-last=Hobson |author-first=Ernest William |author-link=Ernest William Hobson |title=Treatise on Plane Trigonometry |location=Cambridge, UK |date=1911 |page=19}}</ref> -->
<!-- <ref name="Toledo_1917">{{cite book |author-last=de Toledo |author-first=Luis Octavio |author-link=:es:Luis Octavio de Toledo y Zulueta |title=Tradado de Trigonometria |language=es |edition=3rd |location=Madrid |date=1917 |page=64}}</ref> -->
<!-- <ref name="Rothe_1921">{{cite book |author-last=Rothe |author-first=Hermann |author-link=Hermann Rothe |title=Vorlesungen über höhere Mathematik |language=de |location=Vienna |date=1921 |page=261}}</ref> -->
}}

{{Hyperoperations}}
{{Orders of magnitude (time)}}
{{Classes of natural numbers}}
{{Authority control}}

[[Category:Exponentials]]
[[Category:Binary operations]]<!-- when both x and y are arguments for x^y -->
[[Category:Unary operations]]<!-- when taking either x or y in x^y as fixed; e.g. in exp(y) or cube(x) -->