Nathan Fine

{{Infobox person

| name = Nathan Jacob Fine

| birth_date = {{Birth date|1916|10|22}}

| birth_place = Philadelphia, USA

| death_date = {{Death date and age|1994|11|18|1916|10|22}}

| death_place = Deerfield Beach, Florida, USA

| citizenship = American

| alma_mater = University of Pennsylvania

| occupation = Mathematician

| notable_works = Basic Hypergeometric Series and Applications

}}

Nathan Jacob Fine (22 October 1916 in Philadelphia – 18 November 1994 in Deerfield Beach, Florida) was an American mathematician who worked on basic hypergeometric series. He is best known for his lecture notes on the subject which for four decades served as an inspiration to experts in the field until they were finally published as a book. He solved the Jeep problem in 1946.

Nathan Fine retired in 1978 as a professor at Pennsylvania State University. Prior to that he had been on the faculties of the University of Pennsylvania and Cornell University. For a brief period (1946–1947) he also worked at the Operations Evaluation Group, affiliated with the Massachusetts Institute of Technology. Beside the book he published about 40 papers in several fields of mathematics. He is known for the Rogers-Fine identity.{{cite book|chapter-url=https://books.google.com/books?id=3bZQDwAAQBAJ&pg=PA71|chapter=Chapter 9. The Rogers-Fine identity|pages=71–79|title = Topics and Methods in q-Series|isbn = 9789813223387|last1 = Laughlin|first1 = James Mc|date = 22 September 2017}}

Nathan Fine received his Ph.D. in 1946 from University of Pennsylvania, where he was a student of Antoni Zygmund. Fine was at the Institute for Advanced Study for the three academic years 1953–1954, 1958–1959, and 1959–1960.{{cite web|title=Natham J. Fine|website=Institute for Advanced Study|date=9 December 2019 |url=https://www.ias.edu/scholars/nathan-j-fine}} Fine's doctoral students include J. J. Price.

He wrote the book Basic Hypergeometric Series and Applications {{ISBN|0-8218-1524-5}}.{{cite journal|author=Askey, Richard|title=Review: Nathan J. Fine, Basic hypergeometric series and applications|journal=Bull. Amer. Math. Soc. (N.S.)|year=1989| volume=21|issue=1|pages=130–132|url=http://projecteuclid.org/euclid.bams/1183555138|doi=10.1090/s0273-0979-1989-15789-3|doi-access=free}}{{cite book|url=https://books.google.com/books?id=JmzyBwAAQBAJ|title = Basic Hypergeometric Series and Applications|isbn = 9780821815243|last1 = Fine|first1 = Nathan Jacob|year = 1988|postscript=; pbk edition}}

Selected publications

{{cite journal|doi=10.1090/S0002-9904-1944-08085-3|title=The probability that a determinant be congruent to a (mod m)|year=1944|last1=Fine|first1=N. J.|author-mask=2|last2=Niven|first2=Ivan|authorlink2=Ivan M. Niven|journal=Bulletin of the American Mathematical Society|volume=50|issue=2|pages=89–94|doi-access=free}}
{{cite journal|jstor=88084|last1=Fine|first1=Nathan J.|author-mask=2|title=Some New Results on Partitions|journal=Proceedings of the National Academy of Sciences of the United States of America|year=1948|volume=34|issue=12|pages=616–618|doi=10.1073/pnas.34.12.616|pmid=16588844|pmc=1079179|bibcode=1948PNAS...34..616F|doi-access=free}}
{{cite journal|doi=10.1090/S0002-9947-1949-0032833-2|title=On the Walsh functions|year=1949|last1=Fine|first1=N. J.|author-mask=2|journal=Transactions of the American Mathematical Society|volume=65|issue=3|pages=372–414|doi-access=free}}
{{cite journal|doi=10.1090/S0002-9939-1950-0038397-5|title=Proof of a theorem of Jacobi|year=1950|last1=Fine|first1=N. J.|author-mask=2|journal=Proceedings of the American Mathematical Society|volume=1|issue=5|pages=666–667|doi-access=free}}
{{cite journal|doi=10.1090/S0002-9947-1950-0042535-2|title=The generalized Walsh functions|year=1950|last1=Fine|first1=N. J.|author-mask=2|journal=Transactions of the American Mathematical Society|volume=69|pages=66–77|doi-access=free}}
{{cite journal|doi=10.1090/S0002-9939-1951-0043194-1|title=Note on the Hurwitz zeta-function|year=1951|last1=Fine|first1=N. J.|author-mask=2|journal=Proceedings of the American Mathematical Society|volume=2|issue=3|pages=361–364|doi-access=free}}
{{cite journal|doi=10.1090/S0002-9939-1954-0064337-2|title=On the asymptotic distribution of certain sums|year=1954|last1=Fine|first1=N. J.|author-mask=2|journal=Proceedings of the American Mathematical Society|volume=5|issue=2|pages=243–252|doi-access=free}}
{{cite journal|doi=10.1073/pnas.41.8.588|title=Cesaro Summability of Walsh-Fourier Series|year=1955|last1=Fine|first1=N. J.|author-mask=2|journal=Proceedings of the National Academy of Sciences|volume=41|issue=8|pages=588–591|pmid=16578449|pmc=528139|bibcode=1955PNAS...41..588F|doi-access=free}}
{{cite journal|doi=10.1090/S0002-9947-1957-0091371-6|title=Fourier-Stieltjes series of Walsh functions|year=1957|last1=Fine|first1=N. J.|author-mask=2|journal=Transactions of the American Mathematical Society|volume=86|pages=246–255|doi-access=free}}
{{cite journal|doi=10.1090/S0002-9904-1960-10460-0|title=Extension of continuous functions in $\beta N$ |year=1960|last1=Fine|first1=N. J.|author-mask=2|last2=Gillman|first2=L.|authorlink2=Leonard Gillman|journal=Bulletin of the American Mathematical Society|volume=66|issue=5|pages=376–382|doi-access=free}}
{{cite journal|doi=10.1090/S0002-9939-1962-0143172-5|title=Remote points in $\beta R$ |year=1962|last1=Fine|first1=N. J.|author-mask=2|last2=Gillman|first2=L.|journal=Proceedings of the American Mathematical Society|volume=13|pages=29|doi-access=free}}
{{cite journal|doi=10.1090/S0002-9939-1965-0174934-9|title=Uniqueness theorems for periodic functions|year=1965|last1=Fine|first1=N. J.|author-mask=2|last2=Wilf|first2=H. S.|authorlink2=Herbert Wilf|journal=Proceedings of the American Mathematical Society|volume=16|pages=109–114|doi-access=free}}
{{cite journal|doi=10.1090/S0002-9904-1965-11381-7|title=The distribution of the sum of digits (mod p)|year=1965|last1=Fine|first1=N. J.|author-mask=2|journal=Bulletin of the American Mathematical Society|volume=71|issue=4|pages=651–653|doi-access=free}}

References

External links

[https://www.ams.org/notices/199506/fine.pdf "Nathan Fine 1916–1994"] – biography article by George Andrews
[http://mathworld.wolfram.com/FinesEquation.html Fine's Equation] – in MathWorld
[http://www-math.mit.edu/~pak/finefull.pdf "On Fine's Partition Theorems, Dyson, Andrews and Missed Opportunities"] – popular article by Igor Pak
{{MathGenealogy |id=7605}}
{{MacTutor Biography|id=Fine_Nathan}}

Category:1916 births

Category:1994 deaths

Category:20th-century American mathematicians

Category:American mathematical analysts

Category:University of Pennsylvania alumni

Category:University of Pennsylvania faculty

Category:Mathematicians at the University of Pennsylvania

Category:Pennsylvania State University faculty