The functions and , and , and , defined by
which for turns into the Bessel equation.
The series representations are:
The asymptotic representations are:
These functions were introduced by W. Thomson (Lord Kelvin, ).
|||W. Thomson, "Mathematical and physical papers" , 3 , Cambridge Univ. Press (1980) pp. 492|
|||E. Jahnke, F. Emde, F. Lösch, "Tafeln höheren Funktionen" , Teubner (1966)|
|||I.S. Gradshtein, I.M. Ryzhik, "Table of integrals, series and products" , Acad. Press (1973) (Translated from Russian)|
|[a1]||M. Abramowitz, I.A. Stegun, "Handbook of mathematical functions" , Dover, reprint (1965)|
Kelvin functions. A.B. Ivanov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Kelvin_functions&oldid=15392