Editing Bessel function (section)

=== Bourget's hypothesis ===
Bessel himself originally proved that for nonnegative integers {{mvar|n}}, the equation {{math|1=''J''<sub>''n''</sub>(''x'') = 0}} has an infinite number of solutions in {{mvar|x}}.<ref>Bessel, F. (1824), article 14.</ref> When the functions {{math|''J''<sub>''n''</sub>(''x'')}} are plotted on the same graph, though, none of the zeros seem to coincide for different values of {{mvar|n}} except for the zero at {{math|1=''x'' = 0}}. This phenomenon is known as '''Bourget's hypothesis''' after the 19th-century French mathematician who studied Bessel functions. Specifically it states that for any integers {{math|''n'' ≥ 0}} and {{math|''m'' ≥ 1}}, the functions {{math|''J<sub>n</sub>''(''x'')}} and {{math|''J''<sub>''n'' + ''m''</sub>(''x'')}} have no common zeros other than the one at {{math|1=''x'' = 0}}. The hypothesis was proved by [[Carl Ludwig Siegel]] in 1929.<ref>Watson, pp. 484–485.</ref>