On the asymptotic forms of the solutions of ordinary linear differential equations of the third order in a region containing a turning point
Author:
Rudolph E. Langer
Journal:
Trans. Amer. Math. Soc. 80 (1955), 93123
MSC:
Primary 34.0X
MathSciNet review:
0073009
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References 
Similar Articles 
Additional Information
 [1]
Rudolph
E. Langer, The boundary problem of an ordinary
linear differential system in the complex domain, Trans. Amer. Math. Soc. 46 (1939), 151–190 and
Correction, 467 (1939). MR 0000084
(1,15f), http://dx.doi.org/10.1090/S00029947193900000847
 [2]
Hugh
L. Turrittin, Asymptotic Solutions of Certain Ordinary Differential
Equations Associated with Multiple Roots of the Characteristic
Equation, Amer. J. Math. 58 (1936), no. 2,
364–376. MR
1507160, http://dx.doi.org/10.2307/2371046
 [3]
Wolfgang
Wasow, The complex asymptotic theory of a fourth order differential
equation of hydrodynamics, Ann. of Math. (2) 49
(1948), 852–871. MR 0027933
(10,377e)
 [4]
Rudolph
E. Langer, Asymptotic solutions of a differential equation in the
theory of microwave propagation, Comm. Pure Appl. Math.
3 (1950), 427–438. MR 0041314
(12,828g)
 [5]
Wolfgang
Wasow, A study of the solutions of the differential equation
𝑦⁽⁴⁾+𝜆²(𝑥𝑦”+𝑦)=0
for large values of 𝜆, Ann. of Math. (2) 52
(1950), 350–361. MR 0037432
(12,261b)
 [6]
D.
Meksyn, Asymptotic integrals of a fourth order differential
equation containing a large parameter, Proc. London Math. Soc. (2)
49 (1947), 436–457. MR 0024004
(9,436i)
 [7]
D.
Meksyn, Stability of viscous flow between rotating cylinders.
I, Proc. Roy. Soc. London. Ser. A. 187 (1946),
115–128. MR 0019462
(8,415b)
 [8]
Rudolph
E. Langer, The asymptotic solutions of ordinary
linear differential equations of the second order, with special reference
to a turning point, Trans. Amer. Math. Soc.
67 (1949),
461–490. MR 0033420
(11,438b), http://dx.doi.org/10.1090/S00029947194900334202
 [9]
G.
N. Watson, A Treatise on the Theory of Bessel Functions,
Cambridge University Press, Cambridge, England; The Macmillan Company, New
York, 1944. MR
0010746 (6,64a)
 [1]
 R. E. Langer, The boundary problem of an ordinary linear differential system in the complex domain, Trans. Amer. Math. Soc. vol. 46 (1939) pp. 151190. MR 0000084 (1:15f)
 [2]
 H. L. Turrittin, Asymptotic solutions of certain ordinary differential equations associated with multiple roots of the characteristic equation, Amer. J. Math. vol. 58 (1936) pp. 364376. MR 1507160
 [3]
 W. Wasow, The complex asymptotic theory of a fourth order differential equation of hydrodynamics, Ann. of Math. vol. 49 (1948) pp. 852871. MR 0027933 (10:377e)
 [4]
 R. E. Langer, Asymptotic solutions of a differential equation in the theory of microwave propagation, Communications on Pure and Applied Mathematics vol. 3 (1950) pp. 427438. MR 0041314 (12:828g)
 [5]
 W. Wasow, A study of the solutions of the differential equation , for large values of , Ann. of Math. vol. 52 (1950) pp. 350361. MR 0037432 (12:261b)
 [6]
 D. Meksyn, Asymptotic integrals of a fourth order differential equation containing a large parameter, Proc. London Math. Soc. (2) vol. 49 (1947) pp. 436457. MR 0024004 (9:436i)
 [7]
 , Stability of viscous flow between rotating cylinders, Proc. Roy. Soc. London Ser. A vol. 187 (1946) pp. 115128, 480504. MR 0019462 (8:415b)
 [8]
 R. E. Langer, The asymptotic solutions of ordinary linear differential equations of the second order with special reference to a turning point, Trans. Amer. Math. Soc. vol. 67 (1949) pp. 461490. MR 0033420 (11:438b)
 [9]
 G. N. Watson, A treatise on the theory of Bessel functions, 2d ed., Cambridge, New York, 1944. MR 0010746 (6:64a)
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DOI:
http://dx.doi.org/10.1090/S00029947195500730095
PII:
S 00029947(1955)00730095
Article copyright:
© Copyright 1955
American Mathematical Society
