The asymptotic solutions of a linear differential equation of the second order with two turning points

Author:
Rudolph E. Langer

Journal:
Trans. Amer. Math. Soc. **90** (1959), 113-142

MSC:
Primary 34.00

DOI:
https://doi.org/10.1090/S0002-9947-1959-0105530-9

MathSciNet review:
0105530

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References | Similar Articles | Additional Information

**[1]**Nathan Schwid,*The asymptotic forms of the Hermite and Weber functions*, Trans. Amer. Math. Soc. vol. 37 (1935) pp. 339-362. MR**1501790****[2]**A. Erdélyi, M. Kennedy, and J. L. McGregor,*Parabolic cylinder functions of large order*, Journal of Rational Mechanics and Analysis vol. 3 (1954) pp. 459-485. MR**0062875 (16:33c)****[3]**W. E. Johnson,*Asymptotic solutions of a linear second order differential equation with two turning points*, Dissertation, University of Wisconsin, 1952; Bull. Amer. Math. Abstract 58-6-633.**[4]**R. E. Langer,*On the asymptotic solutions of differential equations, with an application to the Bessel functions of large complex order*, Trans. Amer. Math. Soc. vol. 34 (1932) pp. 447-480. MR**1501648****[5]**-,*On the zeros of exponential sums and integrals*, Bull. Amer. Math. Soc. vol. 37 (1931) pp. 213-239. MR**1562129**

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DOI:
https://doi.org/10.1090/S0002-9947-1959-0105530-9

Article copyright:
© Copyright 1959
American Mathematical Society