The idea was introduced in 19821973 by [[W.William J. Lentz]] and was simplified in 1982. Lentz suggested that calculating ratios of spherical Bessel functions of complex arguments can be difficult. He developed a new continued fraction technique for calculating them. This method was an improvement compared to other methods because it eliminated errors on certain terms or provided zero as a result.<ref>{{Cite book|last=J.|first=Lentz, W.|url=http://worldcat.org/oclc/227549426|title=A Simplification of Lentz's Algorithm.|date=August 1982|publisher=Defense Technical Information Center|oclc=227549426}}</ref> The original algorithm assumes that the denominators occurring during execution remain non-zero throughout. Improvements to overcome this limitation include an altered recurrence relation<ref>{{Cite journal|last=Jaaskelainen|first=T.|last2=Ruuskanen|first2=J.|date=1981-10-01|title=Note on Lentz’s algorithm|url=http://dx.doi.org/10.1364/ao.20.003289|journal=Applied Optics|volume=20|issue=19|pages=3289|doi=10.1364/ao.20.003289|issn=0003-6935}}</ref> suggested in 1981 or a simple shift of the denominator by a very small number as suggested in 1986.<ref>{{Cite journal|last=Thompson|first=I.J.|last2=Barnett|first2=A.R.|date=1986|title=Coulomb and Bessel functions of complex arguments and order|url=http://dx.doi.org/10.1016/0021-9991(86)90046-x|journal=Journal of Computational Physics|volume=64|issue=2|pages=490–509|doi=10.1016/0021-9991(86)90046-x|issn=0021-9991}}</ref>
