Asymptotic expansions for the Whittaker functions of large complex order 𝑚

Asymptotic expansions for the Whittaker functions of large complex order $m$
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Trans. Amer. Math. Soc. 78 (1955), 305-328

DOI: https://doi.org/10.1090/S0002-9947-1955-0067248-7

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References

Chieh-Chien Chang, Boa-Teh Chu, and Vivian O’Brien, An asymptotic expansion of the Whittaker function $w_{k,m}(z)$, J. Rational Mech. Anal. 2 (1953), 125–135. MR 51374, DOI 10.1512/iumj.1953.2.52007
Chieh-Chien Chang, Boa-Teh Chu, and Vivian O’Brien, Asymptotic expansion of the Whittaker’s function $W_{k,m}(z)$ for large values of $k,m,z$. I, II, J. Franklin Inst. 255 (1953), 215–236, 319–331. MR 58769, DOI 10.1016/0016-0032(53)90004-0

Asymptotische Darstellung der Whittakerschen Funktionen

Asymptotic representations of confluent hypergeometric functions

Rudolph E. Langer, On the asymptotic solutions of differential equations, with an application to the Bessel functions of large complex order, Trans. Amer. Math. Soc. 34 (1932), no. 3, 447–480. MR 1501648, DOI 10.1090/S0002-9947-1932-1501648-5
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The asymptotic solutions of a certain type of ordinary differential equation