On the construction of related differential equations
Author:
Rudolph E. Langer
Journal:
Trans. Amer. Math. Soc. 81 (1956), 394410
MSC:
Primary 34.0X
MathSciNet review:
0079159
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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
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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
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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
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Robert
W. McKelvey, The solutions of second order linear
ordinary differential equations about a turning point of order
two, Trans. Amer. Math. Soc. 79 (1955), 103–123. MR 0069344
(16,1023f), http://dx.doi.org/10.1090/S00029947195500693447
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Rudolph
E. Langer, On the asymptotic forms of the
solutions of ordinary linear differential equations of the third order in a
region containing a turning point, Trans. Amer.
Math. Soc. 80
(1955), 93–123. MR 0073009
(17,365c), http://dx.doi.org/10.1090/S00029947195500730095
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Rudolph
E. Langer, The solutions of a class of ordinary linear differential
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point, Duke Math. J. 23 (1956), 93–110. MR 0079684
(18,127d)
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Rudolph
E. Langer, Asymptotic solutions of a differential equation in the
theory of microwave propagation, Comm. Pure Appl. Math.
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Wolfgang
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𝑦⁽⁴⁾+𝜆²(𝑥𝑦”+𝑦)=0
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 [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]
 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)
 [4]
 R. W. McKelvey, The solutions of second order linear ordinary differential equations about a turning point of order two, Trans. Amer. Math. Soc. vol. 79 (1955) pp. 103123. MR 0069344 (16:1023f)
 [5]
 R. E. Langer, On the asymptotic forms of the solutions of ordinary linear differential equations of the third order in a region containing a turning point, Trans. Amer. Math. Soc. vol. 80 (1955) pp. 93123. MR 0073009 (17:365c)
 [6]
 , The solutions of a class of ordinary linear differential equations of the third order in a region containing a multiple turning point, to appear in Duke Math. J. MR 0079684 (18:127d)
 [7]
 , Asymptotic solutions of a differential equation in the theory of microwave propagation, Comm. on Pure and Applied Math. vol. 3 (1950) pp. 427438. MR 0041314 (12:828g)
 [8]
 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)
 [9]
 , 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)
 [10]
 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)
 [11]
 , Stability of viscous flow between rotating cylinders, Proc. Royal Soc. London Ser. A. vol. 187 (1946) pp. 115128 and 480504. MR 0019462 (8:415b)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947195600791592
PII:
S 00029947(1956)00791592
Article copyright:
© Copyright 1956
American Mathematical Society
