View source for Richard Bruce Paris

{{Short description|British mathematician}}
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{{Infobox scientist
| name              = Richard Bruce Paris
| image             = Richard_Bruce_Paris_in_2003.png
| caption           = Richard Bruce Paris in 2003
| birth_date        = {{birth date|1946|1|23|df=y}}
| birth_place       = [[Bradford]], UK
| death_date        = {{death date and age|2022|7|8|1946|1|23|df=y}}
| nationality       = British
| fields            = [[Mathematics]]
| workplaces        = [[Abertay University]], Dundee
| alma_mater        = [[University of Manchester]]
| thesis_title      = The Role of the Magnetic Field in Cosmogony
| thesis_url        = https://uomlibrary.access.preservica.com/uncategorized/IO_b843c188-dd73-4ebf-9fbb-4f76dbf7d828
| thesis_year       = 1971
| doctoral_advisor  = [[Leon Mestel]]
| known_for         = [[special functions]], Mellin-Barnes integrals, hyperasymptotics, Hadamard expansions
}}
'''Richard Bruce Paris''' (23 January 1946 – 8 July 2022<ref>{{Cite web |title=Hommage à Richard Bruce Paris, mathématicien - Le Blog de Sylvie Neidinger |url=http://blogdesylvieneidinger.blogspirit.com/archive/2022/07/08/hommage-a-richard-bruce-paris-mathematicien.html |access-date=2023-01-20 |website=blogdesylvieneidinger.blogspirit.com |language=fr}}</ref>) was a British mathematician and [[Reader (academic rank)|reader]] at the [[Abertay University|Abertay University in Dundee]], who specialized in calculus. He also had an honorary readership of the [[University of St Andrews|University of St. Andrews]], Scotland. The research activity of Paris particularly concerned the [[Asymptotic analysis|asymptotics]] of integrals and properties of [[special functions]]. He is the author of ''Hadamard Expansions and Hyperasymptotic Evaluation: An Extension of the Method of Steepest Descent'' as well as the co-author of ''Asymptotics and Mellin-Barnes Integrals'' and of ''Asymptotics of High Order Differential Equations''. In addition, he contributed to the ''NIST Handbook of Mathematical Functions'' and also released numerous papers for ''[[Proceedings of the Royal Society|Proceedings of the Royal Society A]]'', ''Methods and Applications of Analysis'' and the ''[[Journal of Computational and Applied Mathematics]]''.
== Personal life ==
Born in 1946, Richard Bruce Paris was the son of an engineer. He spent his early childhood in the Yorkshire area until his family moved to the [[Wirral Peninsula]], [[Cheshire]], in the mid-1950s, due to the work of his father. There, Paris visited the [[Calday Grange Grammar School]] in [[West Kirby]] to eventually discover his interest in mathematics. <ref name=":0" />
Paris was married to Jocelyne Marie-Louise Neidinger with whom he has a son Simon and a daughter Gaëlle. <ref name=":0">OP-SF NET - Volume 30, No. 1 - Jan. 15, 2023 - The Electronic News Net of the SIAM Activity Group on Orthogonal Polynomials and Special Functions - http://math.nist.gov/opsf</ref>
== Career ==
In 1967, Paris acquired a [[British undergraduate degree classification|first class honours degree]] in [[Mechanical engineering|Mechanical Engineering]] from the [[Victoria University of Manchester]]. He continued his study at the university's department of mathematics, which he graduated as a [[Doctor of Philosophy]] in 1971. <ref name=":0" /> Paris was a doctoral student of the British-Australian astronomer [[Leon Mestel]]''.'' His [[Doctor of Philosophy|PhD]] thesis was finished under the title ''The Role of the Magnetic Field in Cosmogony''. <ref>{{Cite web |title=U376701 {{!}} University of Manchester Library Universal Access |url=https://uomlibrary.access.preservica.com/uncategorized/IO_b843c188-dd73-4ebf-9fbb-4f76dbf7d828 |access-date=2023-01-10 |website=uomlibrary.access.preservica.com}}</ref>
After Paris finished his doctoral thesis, in 1974 he moved to France to work for [[Euratom]] at the Department of Plasma Physics and Controlled Fusion in [[Fontenay-aux-Roses]]. In addition, from the mid-1970s to the mid-1980s, Paris did several research visits in [[Los Alamos National Laboratory|Los Alamos]], USA. Finally, in 1984 he had to move to Southern France, due to a job transfer to [[Cadarache]]. In 1987, Paris quit his job at Euratom and returned to Scotland to work as a senior lecturer at the [[Abertay University|Abertay University in Dundee]]. A year later, in 1988, he received the honorary readership of the [[University of St Andrews|University of St. Andrews]], Scotland. In 1999, he also achieved the degree of a [[Doctor of Science]] at the [[University of Manchester]]. Paris stayed at the University of Abertay, where he eventually obtained the status of a reader, until his retirement in 2010. Yet, this was not the end of his mathematical work but he kept contributing until his unexpected death in July 2022. In fact, one month earlier he shared his final article on [[ResearchGate]]. <ref name=":0" />
In 1986, Paris became an elected fellow of the British [[Institute of Mathematics and its Applications]].<ref name=":1">{{Cite web |title=DLMF: Profile Richard B. Paris ‣ About the Project |url=https://dlmf.nist.gov/about/bio/RBParis |access-date=2023-01-02 |website=dlmf.nist.gov}}</ref>
== Work ==
The work of Paris deals with the asymptotic behaviour of a wide scope of [[special functions]], in many case with a connection to physical problems.
In collaboration with David Kaminski, [[associate professor]] of mathematics at the [[University of Lethbridge]], Paris published the monograph ''Asymptotics and Mellin-Barnes integrals''. It is one of the few textbooks that extensively treats the application of [[Mellin transform|Mellin transforms]] particularly to different asymptotic problems. Mellin-Barnes integrals constitute a special class of contour integrals that feature special functions in the integrand, most frequently products of [[Gamma function|gamma functions]]. Their evaluation relies on the [[residue theorem]] and requires appropriate manipulations of the integration path. The name is due to the mathematicians [[Hjalmar Mellin|R. H. Mellin]] and [[Ernest Barnes|E. W. Barnes]]. Many integrals can be transformed to a Mellin-Barnes representation, by writing their integrands in terms of inverse Mellin transforms. In the context of Laplace-type integrals, this technique provides a powerful alternative to [[Laplace's method]]. In general, however, it admits a broader applicability and much space for modifications. This versatility is shown by means of several examples from [[number theory]] and integrals of higher dimension.<ref>{{Cite book |last=Paris |first=R. B. |url=https://www.worldcat.org/oclc/70756548 |title=Asymptotics and Mellin-Barnes integrals |date=2001 |publisher=Cambridge University Press |others=D. Kaminski |isbn=0-521-79001-8 |location=Cambridge |oclc=70756548}}</ref>
In his monograph ''Hadamard Expansions and Hyperasymptotic Evaluation: An Extension of the Method of Steepest Descent'', by means of theoretical and numerical examples, Paris illustrates the application of [[Laplace's method]] and possibilities to achieve a higher accuracy. The term Hadamard expansions describes a special kind of asymptotic expansions whose coefficients are again series. It refers to the French mathematician [[Jacques Hadamard]] who introduced the first series of this kind in 1908 in his paper ''Sur l'expression asymptotique de la fonction de Bessel''.<ref>{{Cite book |last=Paris |first=R. B. |url=https://www.worldcat.org/oclc/847526828 |title=Hadamard Expansions and Hyperasymptotic Evaluation : an Extension of the Method of Steepest Descents |date=2011 |publisher=Cambridge University Press |isbn=978-1-107-08985-3 |location=Cambridge |oclc=847526828}}</ref>
Paris also organized the chapters 8 and 11, respectively about the [[Incomplete gamma function|incomplete Gamma]] and about the [[Struve function|Struve functions]] and related functions, of the ''NIST Digital Library of Mathematical Functions'' and of the ''NIST Handbook of Mathematical Functions''. He validated the original release in 2010 and was the Associate Editor for his chapters from 2015 until his death.<ref name=":1" />
== Publications ==
* with A. D. Wood: ''Asymptotics of Higher Order Differential Equations'', Longman Scientific and Technical, 1986, ISBN 0-470-20375-7
* with D. Kaminski: ''Asymptotics and Mellin-Barnes Integrals'', Cambridge University Press, 2001, ISBN 978-0-521-79001-7 (vol. 85 of the Encyclopedia of Mathematics and its Applications)
* ''Hadamard Expansions and Hyperasymptotic Evaluation: An Extension of the Method of Steepest Descent'', Cambridge University Press, 2011, ISBN 978-1-107-00258-6 (vol. 141 of the Encyclopedia of Mathematics and its Applications)
* with [[F. W. J. Olver]], [[Richard Askey|R. Askey]] et al.: ''NIST Handbook of Mathematical Functions'', Cambridge University Press, 2010, Hardback ISBN 978-0-521-19225-5, Paperback ISBN 978-0-521-14063-8
== References ==
{{reflist}}
== External links ==
*[https://www.researchgate.net/profile/Richard-Paris-2 Richard Bruce Paris] at ResearchGate
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{{DEFAULTSORT:Paris, Richard Bruce}}
[[Category:1946 births]]
[[Category:2022 deaths]]
[[Category:British mathematicians]]
[[Category:Scientists from Bradford]]