On the construction of related differential equations

Author:
Rudolph E. Langer

Journal:
Trans. Amer. Math. Soc. **81** (1956), 394-410

MSC:
Primary 34.0X

DOI:
https://doi.org/10.1090/S0002-9947-1956-0079159-2

MathSciNet review:
0079159

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References | Similar Articles | Additional Information

**[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. 151-190. 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. 364-376. 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. 461-490. 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. 103-123. 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. 93-123. 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. 427-438. 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. 852-871. 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. 350-361. 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. 436-457. MR**0024004 (9:436i)****[11]**-,*Stability of viscous flow between rotating cylinders*, Proc. Royal Soc. London Ser. A. vol. 187 (1946) pp. 115-128 and 480-504. MR**0019462 (8:415b)**

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DOI:
https://doi.org/10.1090/S0002-9947-1956-0079159-2

Article copyright:
© Copyright 1956
American Mathematical Society