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On the continued fractions which represent the functions of Hermite and other functions defined by differential equations

Published online by Cambridge University Press:  20 January 2009

E. T. Whittaker
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The functions of Hermite, which are the same as the functions associated with the parabolic cylinder in harmonic analysis, may be defined* by the differential equation which they satisfy, namely,

where n denotes any constant.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , February 1913 , pp. 65 - 74
Copyright
Copyright © Edinburgh Mathematical Society 1913

References

* Cf. Hermite, , Comples Sendus 58 (1864), pp. 93, 266.Google Scholar

Whittker, , Proc. Load. Math. Soc. 35 (1903), p. 417.Google Scholar

Myller-Lebedeff, , Math. Ann. 64 (1907), p. 388.CrossRefGoogle Scholar

Watson, , Proc. Land. Math. Soc. (2) 8 (1910), p. 393.CrossRefGoogle Scholar

Curzon, , Proc. Load. Math. Soc. (2) 12 (1912), p. 236.Google Scholar

* Cf. a paper by the present writer in Bull. Amir. Math. Soc. (2) 10 (1903), p. 126.Google Scholar