Editing Bessel function (section)

=== Transcendence ===
Siegel proved in 1929 that when ''ν'' is rational, all nonzero roots of {{math|''J''<sub>''ν''</sub>(x)}} and {{math|''J''{{'}}<sub>''ν''</sub>(x)}} are [[transcendental number|transcendental]],<ref name="lorch"/> as are all the roots of {{math|''K''<sub>''ν''</sub>(x)}}.<ref name="euclid"/> It is also known that all roots of the higher derivatives <math>J_\nu^{(n)}(x)</math> for {{math|''n'' ≤ 18}} are transcendental, except for the special values <math>J_1^{(3)}(\pm\sqrt3) = 0</math> and <math>J_0^{(4)}(\pm\sqrt3) = 0</math>.<ref name="lorch">{{cite journal |last1=Lorch |first1=Lee |last2=Muldoon |first2=Martin E. |title=Transcendentality of zeros of higher dereivatives of functions involving Bessel functions |journal=International Journal of Mathematics and Mathematical Sciences |date=1995 |volume=18 |issue=3 |pages=551–560 |doi=10.1155/S0161171295000706 |doi-access=free}}</ref>