From Wikipedia, the free encyclopedia
American mathematician (1894–1968)
Rudolf Ernest Langer (8 March 1894 – 11 March 1968) was an American
mathematician , known for the
Langer correction and as a president of the
Mathematical Association of America .
[1]
Career
Langer, the elder brother of
William L. Langer and
Walter Charles Langer , earned his PhD in 1922 from
Harvard University under
G. D. Birkhoff . He taught mathematics at
Dartmouth College from 1922 to 1925. From 1927 to 1964 he was a mathematics professor at the
University of Wisconsin-Madison and, from 1942 to 1952, the chair of the mathematics department.
[1] From 1956 to 1963 he was the director of the
Army Mathematics Research Center ; he was succeeded as director by
J. Barkley Rosser .
[2] Langer's doctoral students include
Nicholas D. Kazarinoff ,
Homer Newell, Jr. , and
Henry Scheffé .
Langer was a colleague of American physicist
Carl David Anderson , discoverer of the
positron , and was one of the few people to have read
Dirac ’s work on the anti-electron and made a connection. He sent a short paper to
Science making connections between the new observations and Dirac’s theories, putting forth imaginative claims such as that the proton is made of a neutron and a positron. His paper was not taken seriously.
[3]
Works
Langer, Rudolph E. (1923).
"Developments associated with a boundary problem not linear in the parameter" . Trans. Amer. Math. Soc . 25 (2): 155–172.
doi :
10.1090/s0002-9947-1923-1501235-3 .
MR
1501235 .
Langer, R. E. (1926).
"On the momental constants of a summable function" . Trans. Amer. Math. Soc . 28 (1): 168–182.
doi :
10.1090/s0002-9947-1926-1501338-6 .
MR
1501338 .
Langer, Rudolph E. (1926).
"On the theory of integral equations with discontinuous kernels" . Trans. Amer. Math. Soc . 28 (4): 585–639.
doi :
10.1090/s0002-9947-1926-1501367-2 .
MR
1501367 .
Langer, Rudolph E. (1929).
"The boundary problem associated with a differential equation in which the coefficient of the parameter changes sign" . Trans. Amer. Math. Soc . 31 (1): 1–24.
doi :
10.1090/s0002-9947-1929-1501464-4 .
MR
1501464 .
Langer, R. E. (1931).
"On the zeros of exponential sums and integrals" . Bull. Amer. Math. Soc . 37 (4): 213–239.
doi :
10.1090/s0002-9904-1931-05133-8 .
MR
1562129 .
Langer, Rudolph E. (1931).
"On the asymptotic solutions of ordinary differential equations, with an application to the Bessel functions of large order" . Trans. Amer. Math. Soc . 33 (1): 23–64.
doi :
10.1090/s0002-9947-1931-1501574-0 .
MR
1501574 .
Langer, Rudolph E. (1932).
"On the asymptotic solutions of differential equations, with an application to the Bessel functions of large complex order" . Trans. Amer. Math. Soc . 34 (3): 447–480.
doi :
10.1090/s0002-9947-1932-1501648-5 .
MR
1501648 .
Langer, R. E. (1933).
"On an inverse problem in differential equations" . Bull. Am. Math. Soc . 39 (10): 814–820.
doi :
10.1090/s0002-9904-1933-05752-x .
MR
1562734 .
"The asymptotic solutions of ordinary differential equations of the second order, with special reference to the Stokes phenomenon" . Bull. Amer. Math. Soc . 40 (8): 545–582. 1934.
doi :
10.1090/s0002-9904-1934-05913-5 .
MR
1562910 .
Langer, Rudolph E. (1934).
"The solutions of the Mathieu equation with a complex variable and at least one parameter large" . Trans. Amer. Math. Soc . 36 (3): 637–710.
doi :
10.1090/s0002-9947-1934-1501760-2 .
MR
1501760 .
Langer, Rudolph E. (1935).
"On the asymptotic solutions of ordinary differential equations, with reference to the Stokes' phenomenon about a singular point" . Trans. Amer. Math. Soc . 37 (3): 397–416.
doi :
10.1090/s0002-9947-1935-1501793-7 .
MR
1501793 .
Langer, R. E. (1936).
"On determination of earth conductivity from observed surface potentials" . Bull. Am. Math. Soc . 42 (10): 747–754.
doi :
10.1090/s0002-9904-1936-06420-7 .
MR
1563417 .
Langer, Rudolph E. (1937). "On the connection formulas and the solutions of the wave equations". Phys. Rev . 51 (8): 669–676.
Bibcode :
1937PhRv...51..669L .
doi :
10.1103/physrev.51.669 .
Langer, Rudolph E. (1949).
"The asymptotic solutions of ordinary linear differential equations of the second order, with special reference to a turning point" . Trans. Amer. Math. Soc . 67 (2): 461–490.
doi :
10.1090/s0002-9947-1949-0033420-2 .
MR
0033420 .
"Differential Equations, Ordinary". Encyclopædia Britannica . Vol. 7 (1967 and 1968 ed.). pp. 407–412.
References
External links
International National Academics Other