For 
,
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is a zeroth order Bessel function of
the first kind and 
is a zeroth order Bessel
function of the second kind.
Mehler's Bessel Function Formula
See also
Bessel Function of the First Kind, Bessel Function of the Second KindExplore with Wolfram|Alpha
References
Itô, K. (Ed.). Encyclopedic Dictionary of Mathematics, 2nd ed., Vol. 2. Cambridge, MA: MIT Press, p. 1802, 1986.Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1472, 1980.Referenced on Wolfram|Alpha
Mehler's Bessel Function FormulaCite this as:
Weisstein, Eric W. "Mehler's Bessel Function Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MehlersBesselFunctionFormula.html