When 
is an integer 
, then 
and 
have no common zeros other than at 
for 
an integer 
, where 
is a Bessel
function of the first kind. The theorem has been proved true for 
2, 3, and 4.
Bourget's Hypothesis
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References
Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1966.Referenced on Wolfram|Alpha
Bourget's HypothesisCite this as:
Weisstein, Eric W. "Bourget's Hypothesis." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BourgetsHypothesis.html