J Boersma and M L Glasser 2005 J. Phys. A: Math. Gen. 38 1687 doi:10.1088/0305-4470/38/8/005
A differentiation formula for spherical Bessel functions
J Boersma1,3 and M L Glasser2
Show affiliationsThe differentiation formula ![\fl
\left(1-\frac{\sqrt{z^2+a^2}}{z} \frac{\rm d}{{\rm d}z}\right)^n
[z^{n-1/2}K_{n-1/2}(z)] = \big(z+\sqrt{z^2+a^2}\big)^n z^{-1/2}K_{1/2}(z)](http://ej.iop.org/images/0305-4470/38/8/005/jpa187589ueq01.gif)
is derived, where Kn−1/2(z) is a modified spherical Bessel function and a is an arbitrary constant.
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Issue 8 (25 February 2005)
Received 5 October 2004, in final form 23 November 2004
Published 9 February 2005
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A differentiation formula for spherical Bessel functions
J Boersma and M L Glasser 2005 J. Phys. A: Math. Gen. 38 1687
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