The idea was introduced in 1973 by William J. Lentz<ref name=":0" /> and was simplified by him in 1982.<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> Lentz suggested that calculating ratios of spherical Bessel functions of complex arguments can be difficult. He developed a new continued fraction technique for calculating themthe ratios of spherical Bessel functions of consecutive order. This method was an improvement compared to other methods because itstarted eliminatedfrom errorsthe onbeginning certainof termsthe orcontinued providedfraction zerorather asthan the tail, had a resultbuilt-in check for convergence, and was numerically stable. The original algorithm assumesuses thatalgebra theto denominatorsbypass occurringa duringzero executionin remaineither non-zerothe numerator or throughoutdenominator. Simpler Improvements to overcome thisunwanted limitationzero terms include an altered recurrence relation<ref>{{Cite journal|last1=Jaaskelainen|first1=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=3289–3290|doi=10.1364/ao.20.003289|pmid=20333144 |bibcode=1981ApOpt..20.3289J |issn=0003-6935}}</ref> suggested by Jaaskelainen and Ruuskanen in 1981 or a simple shift of the denominator by a very small number as suggested by Thompson and Barnett in 1986.<ref name=":1">{{Cite journal|last1=Thompson|first1=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|bibcode=1986JCoPh..64..490T |issn=0021-9991}}</ref>
