Contributions to the theory of Hermitian series. II. The representation problem

Contributions to the theory of Hermitian series. II. The representation problem
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by Einar Hille

Trans. Amer. Math. Soc. 47 (1940), 80-94

DOI: https://doi.org/10.1090/S0002-9947-1940-0000871-3

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References

Einar Hille, A class of reciprocal functions, Ann. of Math. (2) 27 (1926), no. 4, 427–464. MR 1502747, DOI 10.2307/1967695
Einar Hille, Contributions to the theory of Hermitian series, Duke Math. J. 5 (1939), 875–936. MR 870
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

Zur Theorie der asymptotischen Potenzreihen

Über die Eigenschaften analytischer Funktionen in der Umgebung einer singulären Stelle oder Linie

Nathan Schwid, The asymptotic forms of the Hermite and Weber functions, Trans. Amer. Math. Soc. 37 (1935), no. 2, 339–362. MR 1501790, DOI 10.1090/S0002-9947-1935-1501790-1
Gabor Szegö, Orthogonal Polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, New York, 1939. MR 0000077, DOI 10.1090/coll/023
Otto Volk, Über die Entwicklung von Funktionen einer komplexen Veränderlichen nach Funktionen, die einer linearen Differentialgleichung zweiter Ordnung mit einem Parameter genügen, Math. Ann. 86 (1922), no. 3-4, 296–316 (German). MR 1512093, DOI 10.1007/BF01457991

The harmonic functions associated with the parabolic cylinder

On the functions associated with the parabolic cylinder in harmonic analysis

Modern Analysis