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Milton Abramowitz (19 February 1915 – 5 July 1958)[1] was an American mathematician at the National Bureau of Standards (NBS) who, with Irene Stegun, edited a classic book of mathematical tables called Handbook of Mathematical Functions, widely known as “Abramowitz and Stegun“.

Education and career

Abramowitz was born in Brooklyn, NY. He received a B. A. in mathematics in 1937 from Brooklyn College. He joined the NBS Math Tables Project in 1938, first as a member of the technical planning staff, while continuing his graduate studies at Brooklyn College in the evening. He obtained his M. A. in mathematics in 1940 and went on to attend the Ph.D. program in Mathematics at New York University, where he was supervised by Kurt Otto Friedrichs and graduated in 1948. [2][3] In 1954, Abramowitz became the Chief of the Computation Laboratory of the NBS Applied Mathematics Division.[4] In 1958, he died while mowing the lawn of his home in suburban Washington, when the heat caused a heart attack.[5][1]

Research

In 1953, Abramowitz studied the behavior of the integral as a function of x, which was previously studied in physical problems where particle velocities were distributed according to a Maxwellian distribution.[6] He found a power series expression for this function useful for small x, as well as the asymptotic for large x.[6] More generally, he showed that the integral asymptotes to where for large x.[6]

In 1957, Abramowitz and Stegun proposed an algorithm for numerically computing the values of Bessel functions and in the regime where both the index n and the argument x were large, using a recurrence relation.[7]

Coulomb wave functions

In 1954, Abramowitz and H. A. Antosiewicz studied the Coulomb wave functions in the form . By expressing them in terms of the Airy functions as and , they were able to expand the functions as a power series in x.[8] In the same issue of Physical Review, Abramowitz and Philip Rabinowitz were able to find an expansion for the Coulomb wave functions in the special case using the method of steepest descent.[9]

Legacy

At the time of Abramowitz’ death, the book was not yet completed but was well underway. Irene Stegun took over management of the project and was able to finish the work by 1964, working under the direction of the NBS Chief of Numerical Analysis Philip J. Davis, who was also a contributor to the book. The major work of producing reliable mathematical tables, was part of the WPA project of Franklin Roosevelt.

In his memory, the Abramowitz Award is granted by the University of Maryland, College Park to students “for superior competence and promise in the field of mathematics and its applications.” Winners of this award include Charles Fefferman and Sergey Brin.[10]

References

  1. ^ a b “Notes – Milton Abramowitz (1915–1958)”. Mathematical Tables and Other Aids to Computation. 12 (63): 264–267. 1958. ISSN 0891-6837. JSTOR 2002029.
  2. ^ F. Boisvert and D. W. Lozier (2001) Handbook of Mathematical Functions, in A Century of Excellence in Measurements Standards and Technology (D. R. Lide, ed.), CRC Press, pp. 135–139
  3. ^ “Milton Abramowitz”. Journal of the Washington Academy of Sciences. 48 (8): 266–266. 1958. ISSN 0043-0439.
  4. ^ “Notes”. Mathematical Tables and Other Aids to Computation. 12 (63): 264–267. 1958. ISSN 0891-6837.
  5. ^ Grier, David Alan (August 2006). “Irene Stegun, the Handbook of Mathematical Functions, and the Lingering Influence of the New Deal”. The American Mathematical Monthly. 113 (7): 585–597. doi:10.1080/00029890.2006.11920341. ISSN 0002-9890.
  6. ^ a b c Abramowitz, Milton (April 1953). “Evaluation of the Integral”. Journal of Mathematics and Physics. 32 (1–4): 188–192. doi:10.1002/sapm1953321188. ISSN 0097-1421.
  7. ^ Stegun, Irene A.; Abramowitz, Milton (1957). “Generation of Bessel Functions on High Speed Computers”. Mathematical Tables and Other Aids to Computation. 11 (60): 255–257. doi:10.2307/2001944. ISSN 0891-6837.
  8. ^ Abramowitz, Milton; Antosiewicz, H. A. (1954-10-01). “Coulomb Wave Functions in the Transition Region”. Physical Review. 96 (1): 75–77. doi:10.1103/PhysRev.96.75. ISSN 0031-899X.
  9. ^ Abramowitz, Milton; Rabinowitz, Philip (1954-10-01). “Evaluation of Coulomb Wave Functions along the Transition Line”. Physical Review. 96 (1): 77–79. doi:10.1103/PhysRev.96.77. ISSN 0031-899X.
  10. ^ “Mathematics Department Awards”. University of Maryland. Retrieved 2021-08-03.