Jump to content

Eduard Heine: Difference between revisions

From Wikipedia, the free encyclopedia
Browse history interactively
← Previous edit
Content deleted Content added
VisualWikitext
Ri'Bassa (talk | contribs)
225 edits
Reword
 
(33 intermediate revisions by 27 users not shown)
Line 1: Line 1:
{{Short description|German mathematician (1821–1881)}}
{{Infobox scientist
{{Infobox scientist
| name = Eduard Heine
| name = Eduard Heine
| image = Heinrich Eduard Heine 1.jpg
| image = Heinrich Eduard Heine 1.jpg
| image_size = 250px
| image_size = 250px
| caption = Heinrich Eduard Heine
| caption = Heinrich Eduard Heine
| birth_date = {{birth date|1821|3|16|df=y}}
| birth_date = {{birth date|1821|3|16|df=y}}
| birth_place = [[Berlin]], [[Prussia]]
| birth_place = [[Berlin]], [[Prussia]]
| death_date ={{death date and age|1881|10|21|1821|3|15|df=y}}
| death_date = {{death date and age|1881|10|21|1821|3|15|df=y}}
| death_place = [[Halle (Saale)|Halle]], [[Prussia]]
| death_place = [[Halle (Saale)|Halle]], [[Prussia]]
| residence = [[Prussia]]
| nationality = [[Germany|German]]
| nationality = [[Germany|German]]
| field = [[Mathematician]]
| work_institution = [[University of Bonn]]<br/>[[University of Halle]]
| field = [[Mathematician]]
| work_institution = [[University of Bonn]]<br/>[[University of Halle]]
| alma_mater = [[University of Berlin]]
⚫
| doctoral_advisor = [[Enno Dirksen]]<br/>[[Martin Ohm]]
| alma_mater = [[University of Berlin]]
⚫
| doctoral_students =
⚫
| doctoral_advisor = [[Enno Dirksen]]<br/>[[Martin Ohm]]
⚫
| notable_students =
| influences = [[Peter Gustav Lejeune Dirichlet]]
⚫
| known_for = [[Uniform continuity]]<br/>[[Heine–Borel theorem]]
⚫
| doctoral_students =
⚫
| prizes = Gauss Medal
⚫
| notable_students =
⚫
| footnotes =
⚫
| known_for = [[Uniform continuity]]
⚫
| prizes = Gauss medal
| religion = <!-- (Insert religious belief system/affiliation) -->
⚫
| footnotes =
}}
}}


'''Heinrich Eduard Heine''' (March 16, 1821, [[Berlin]]&ndash;October 21, 1881, [[Halle (Saale)|Halle]]) was a [[Germany|German]] [[mathematics|mathematician]].
'''Heinrich Eduard Heine''' (16 March 1821 &ndash; 21 October 1881) was a German [[mathematician]].


Heine became known for results on [[special function]]s and in [[real analysis]]. In particular, he authored an important treatise on [[spherical harmonics]] and [[Legendre functions]] (''Handbuch der Kugelfunctionen''). He also investigated [[basic hypergeometric series]]. He introduced the [[Mehler–Heine formula]].
Heine became known for results on [[special function]]s and in [[real analysis]]. In particular, he authored an important treatise on [[spherical harmonics]] and [[Legendre functions]] (''Handbuch der Kugelfunctionen''). He also investigated [[basic hypergeometric series]]. He introduced the [[Mehler–Heine formula]].


==Biography==
==Biography==
Heinrich Eduard Heine was born on 16 March 1821 in Berlin, as the eighth child of banker Karl Heine and his wife Henriette Märtens. Eduard was initially [[home schooled]], then studied at the Friedrichswerdersche [[Gymnasium (Germany)|Gymnasium]] and Köllnische Gymnasium in Berlin.<ref name=Narins>{{cite book| last = Narins| first = Brigham | title=World of mathematics | year=2001| publisher=Gale Group| location = | isbn= 978-0-7876-5064-3| pages= 289}}</ref> In 1838, after graduating from gymnasium, he enrolled at the [[University of Berlin]], but transferred to the [[University of Göttingen]] to attended the mathematics lectures of [[Carl Friedrich Gauss]] and [[Moritz Stern]]. In 1840 Heine returned to Berlin, where he studied mathematics under [[Peter Gustav Lejeune Dirichlet]], while also attending classes of [[Jakob Steiner]] and [[Johann Franz Encke]]. In 1842 he was an awarded a [[Ph.D.]] by the University of Berlin for a thesis on [[differential equations]] submitted with [[Enno Dirksen]] and [[Martin Ohm]] as advisors. Heine dedicated the doctoral thesis to his professor Gustav Dirichlet. Next he went to the [[University of Königsberg]] to participate in the mathematical seminar of [[Carl Gustav Jacob Jacobi|Carl Gustav Jacobi]], while also following [[mathematical physics]] classes of [[Franz Ernst Neumann]]. In [[Königsberg]] Heine got in contact with fellow students [[Gustav Kirchhoff]] and [[Philipp Ludwig von Seidel]].<ref name=Halle>{{cite web | last = Goebel | first = M. | authorlink = |author2=Ka Richter |author3=H. Schlosser | title = Heinrich Eduard Heine (1821–1881) | work = | publisher = [[University of Halle]] | url = http://www.mathematik.uni-halle.de/history/heine/index.html | doi = | accessdate = 2011-12-07}}</ref>
Heinrich Eduard Heine was born on 16 March 1821 in Berlin, as the eighth child of banker Karl Heine and his wife Henriette Märtens. Eduard was initially [[home schooled]], then studied at the Friedrichswerdersche [[Gymnasium (Germany)|Gymnasium]] and Köllnische Gymnasium in Berlin.<ref name=Narins>{{cite book| last = Narins| first = Brigham | title=World of mathematics | year=2001| publisher=Gale Group| isbn= 978-0-7876-5064-3| pages= 289}}</ref> In 1838, after graduating from gymnasium, he enrolled at the [[University of Berlin]], but transferred to the [[University of Göttingen]] to attend the mathematics lectures of [[Carl Friedrich Gauss]] and [[Moritz Stern]]. In 1840 Heine returned to Berlin, where he studied mathematics under [[Peter Gustav Lejeune Dirichlet]], while also attending classes of [[Jakob Steiner]] and [[Johann Franz Encke]]. In 1842 he was awarded a [[PhD]] by the University of Berlin for a thesis on [[differential equations]] submitted with [[Enno Dirksen]] and [[Martin Ohm]] as advisors. Heine dedicated the doctoral thesis to his professor Gustav Dirichlet. Next he went to the [[University of Königsberg]] to participate in the mathematical seminar of [[Carl Gustav Jacob Jacobi|Carl Gustav Jacobi]], while also following [[mathematical physics]] classes of [[Franz Ernst Neumann]]. In [[Königsberg]] Heine got in contact with fellow students [[Gustav Kirchhoff]] and [[Philipp Ludwig von Seidel]].<ref name=Halle>{{cite web | last = Goebel | first = M. |author2=Ka Richter |author3=H. Schlosser | title = Heinrich Eduard Heine (1821–1881) | publisher = [[University of Halle]] | url = http://www.mathematik.uni-halle.de/history/heine/index.html | access-date = 2011-12-07}}</ref>


In 1844 Heine went for a teaching position at the [[University of Bonn]], passing his [[habilitation]] and starting as a [[privatdozent]]. He continued his research in mathematics in Bonn and, in 1848, was promoted to [[extraordinary professor]]. In 1850 he married Sophie Wolff, the daughter of a Berlin merchant; the couple had five children, four daughters and one son. In 1856 Heine moved as a full professor to the [[University of Halle]], where he remained for the rest of his life. From 1864 to 1865, he served as a rector of the university. In 1875 the University of Göttingen offered Heine a mathematics chair but he decided to reject the offer and remain in Halle. In 1877, at the centenary of Gauss' birth, he was awarded the Gauss medal for his research. Eduard Heine died on 21 October 1881 in Halle.<ref name=Halle/>
In 1844 Heine went for a teaching position at the [[University of Bonn]], passing his [[habilitation]] and starting as a [[privatdozent]]. He continued his research in mathematics in Bonn and, in 1848, was promoted to [[extraordinary professor]]. In 1850 he married Sophie Wolff, the daughter of a Berlin merchant; the couple had five children, four daughters and one son. In 1856 Heine moved as a full professor to the [[University of Halle]], where he remained for the rest of his life. From 1864 to 1865, he served as a rector of the university. In 1875, the University of Göttingen offered Heine a mathematics chair but he decided to reject the offer and remain in Halle. In 1877, at the centenary of Gauss's birth, he was awarded the Gauss Medal for his research.<ref name=Halle/> Eduard Heine died on 21 October 1881 in Halle.<ref name=Halle/>


==Selected Works==
==Selected works==
* [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN31520639X De aequationibus nonnullis differentialibus] (Berlin, 1842)
* [http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN31520639X De aequationibus nonnullis differentialibus] (Berlin, 1842)
* [http://books.google.com/books?id=YE8DAAAAQAAJ&pg=PA3&dq=Eduard+Heine&hl=en#PPR1,M1 Handbuch der Kugelfunctionen] (G. Reimer, Berlin, 1861)
* [https://books.google.com/books?id=YE8DAAAAQAAJ&pg=PA3&dq=Eduard+Heine&hl=en#PPR1,M1 Handbuch der Kugelfunctionen] (G. Reimer, Berlin, 1861)
* [http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=01990001&view=50&frames=0&seq=4 Handbuch der Kugelfunctionen, Theorie und Anwendungen (Volume 1)] (2nd ed., G. Reimer, Berlin, 1878)
* [http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=01990001&view=50&frames=0&seq=4 Handbuch der Kugelfunctionen, Theorie und Anwendungen (Volume 1)] (2nd ed., G. Reimer, Berlin, 1878)
* [http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=01410002&seq=4 Handbuch der Kugelfunctionen, Theorie und Anwendungen (Volume 2)] (2nd ed., G. Reimer, Berlin, 1881)
* [http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=01410002&seq=4 Handbuch der Kugelfunctionen, Theorie und Anwendungen (Volume 2)] (2nd ed., G. Reimer, Berlin, 1881)


==See also==
==See also==
*[[Basic hypergeometric series]]
*[[Cauchy–Binet formula#Continuous version|Andréief–Heine identity]]
*[[Heine–Borel theorem]]
*[[Heine–Borel theorem]]
*[[Heine–Cantor theorem]]
*[[Heine–Cantor theorem]]
*[[Continuous function#Heine definition of continuity|Heine definition of continuity]]
*[[Continuous function#Heine definition of continuity|Heine definition of continuity]]
*[[Heine's Reciprocal Square Root Identity]]
*[[Heine's Reciprocal Square Root Identity]]
*[[Heine–Stieltjes polynomials]]
*[[Formalism (philosophy of mathematics)]]
*[[Limit of a function]]
*[[List of things named after Eduard Heine]]


== References ==
== References ==
Line 53: Line 57:
{{Authority control}}
{{Authority control}}


{{Persondata
| NAME = Heine, Eduard
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = German mathematician
| DATE OF BIRTH = 1821
| PLACE OF BIRTH = [[Berlin]], [[Prussia]]
| DATE OF DEATH = 1881
| PLACE OF DEATH = Halle, Prussia
}}
{{DEFAULTSORT:Heine, Eduard}}
{{DEFAULTSORT:Heine, Eduard}}
[[Category:1821 births]]
[[Category:1821 births]]
[[Category:1881 deaths]]
[[Category:1881 deaths]]
[[Category:German mathematicians]]
[[Category:19th-century German mathematicians]]
[[Category:19th-century German mathematicians]]
[[Category:Mathematical analysts]]
[[Category:German mathematical analysts]]
[[Category:People from Berlin]]
[[Category:Scientists from Berlin]]
[[Category:People from the Province of Brandenburg]]
[[Category:Köllnisches Gymnasium alumni]]
[[Category:University of Göttingen alumni]]
[[Category:University of Göttingen alumni]]
[[Category:Humboldt University of Berlin alumni]]
[[Category:Humboldt University of Berlin alumni]]
[[Category:University of Königsberg alumni]]
[[Category:University of Königsberg alumni]]
[[Category:University of Bonn faculty]]
[[Category:Academic staff of the University of Bonn]]
[[Category:Martin Luther University of Halle-Wittenberg faculty]]
[[Category:Academic staff of the Martin Luther University of Halle-Wittenberg]]
[[Category:Mathematicians from the Kingdom of Prussia]]

Latest revision as of 16:29, 10 June 2024

Eduard Heine
Heinrich Eduard Heine
Born(1821-03-16)16 March 1821
Berlin, Prussia
Died21 October 1881(1881-10-21) (aged 60)
Halle, Prussia
NationalityGerman
Alma materUniversity of Berlin
Known forUniform continuity
Heine–Borel theorem
AwardsGauss Medal
Scientific career
FieldsMathematician
InstitutionsUniversity of Bonn
University of Halle
Doctoral advisorEnno Dirksen
Martin Ohm

Heinrich Eduard Heine (16 March 1821 – 21 October 1881) was a German mathematician.

Heine became known for results on special functions and in real analysis. In particular, he authored an important treatise on spherical harmonics and Legendre functions (Handbuch der Kugelfunctionen). He also investigated basic hypergeometric series. He introduced the Mehler–Heine formula.

Biography

[edit]

Heinrich Eduard Heine was born on 16 March 1821 in Berlin, as the eighth child of banker Karl Heine and his wife Henriette Märtens. Eduard was initially home schooled, then studied at the Friedrichswerdersche Gymnasium and Köllnische Gymnasium in Berlin.[1] In 1838, after graduating from gymnasium, he enrolled at the University of Berlin, but transferred to the University of Göttingen to attend the mathematics lectures of Carl Friedrich Gauss and Moritz Stern. In 1840 Heine returned to Berlin, where he studied mathematics under Peter Gustav Lejeune Dirichlet, while also attending classes of Jakob Steiner and Johann Franz Encke. In 1842 he was awarded a PhD by the University of Berlin for a thesis on differential equations submitted with Enno Dirksen and Martin Ohm as advisors. Heine dedicated the doctoral thesis to his professor Gustav Dirichlet. Next he went to the University of Königsberg to participate in the mathematical seminar of Carl Gustav Jacobi, while also following mathematical physics classes of Franz Ernst Neumann. In Königsberg Heine got in contact with fellow students Gustav Kirchhoff and Philipp Ludwig von Seidel.[2]

In 1844 Heine went for a teaching position at the University of Bonn, passing his habilitation and starting as a privatdozent. He continued his research in mathematics in Bonn and, in 1848, was promoted to extraordinary professor. In 1850 he married Sophie Wolff, the daughter of a Berlin merchant; the couple had five children, four daughters and one son. In 1856 Heine moved as a full professor to the University of Halle, where he remained for the rest of his life. From 1864 to 1865, he served as a rector of the university. In 1875, the University of Göttingen offered Heine a mathematics chair but he decided to reject the offer and remain in Halle. In 1877, at the centenary of Gauss's birth, he was awarded the Gauss Medal for his research.[2] Eduard Heine died on 21 October 1881 in Halle.[2]

Selected works

[edit]

See also

[edit]

References

[edit]
  1. ^ Narins, Brigham (2001). World of mathematics. Gale Group. p. 289. ISBN 978-0-7876-5064-3.
  2. ^ a b c Goebel, M.; Ka Richter; H. Schlosser. "Heinrich Eduard Heine (1821–1881)". University of Halle. Retrieved 2011-12-07.
[edit]
Retrieved from "https://en.wikipedia.org/enwiki/w/index.php?title=Eduard_Heine&oldid=1228323491"