Bateman function: Difference between revisions

Revision as of 11:45, 17 October 2021

Revision as of 13:10, 17 October 2021

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*<math>k_{2n}(x)=0</math> for <math>x<0</math> if <math>n</math> is a positive integer

*<math>k_1(x) = \frac{2x}{\pi} [K_1(x) + K_0(x)], \ x<0</math>, where <math>K_n(-x)</math> is the [[Modified Bessel function of the second kind]].

For a recent survey of the Bateman and related functions see 4 .

For the asymptotic expansion of the Bateman and Havelock

functions of large order and argument, see the recent E-print 5.

==References==

{{Reflist}}

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“The Bateman functions revisited after 90 years – A survey of old and new results”,

Mathematics (MDPI), Vol 9 (2021), 1273/1-27; DOI: 10.3390/math9111273

E-print arXiv: 2104.08596

5. R.B. Paris: "The asymptotic expansion of the Bateman and Havelock

functions of large order and argument", E-print arXiv:2109.00529