Proceedings of the Edinburgh Mathematical Society
- Proceedings of the Edinburgh Mathematical Society / Volume 38 / February 1919, pp 10-19
- Copyright © Edinburgh Mathematical Society 1919
- DOI: http://dx.doi.org/10.1017/S0013091500035537 (About DOI), Published online: 20 January 2009
Research Article
The Modified Bessel Function Kn(z)
Dr T. M. MacRobert
Gray and Mathews, in their treatise on Bessel Functions, define the function Kn(z) to be
We shall denote this function by Vn(z). This definition only holds when z is real, and R(n)≧0. The asymptotic expansion of the function is also given; but the proof, which is said to be troublesome and not very satisfactory, is omitted. Basset (Proc. Camb. Phil. Soc., Vol. 6) gives a similar definition of the function.
(Received February 13 1919)
Notes
* Of. Maodonald, Proc. London Math. Soc., XXX.
* Cf. MacRobert's Functions of a Complex Variable, p. 239.
† Cf. Whittaker and Watson, Analysis, p. 376.
* Cf. Fourier, Théorie Analytique de la Chaleur, Ch. VI., Gray & Mathews, Ch. V., and Clifford, Mathematical Papers, p. 346.
* Cf. Macdonald, Proc. London Math. Soc., XXX.
* Kugelfunctionen, p. 237.
* Cf. Macdonald, Proc. London Math. Soc., XXX., p. 170, and Hardy, Quarterly Journal, XXXIX.
* Cf. Whittaker and Watson, Analysis, Chapter XVI.
