Undergrad How to calculate this Bessel's terms limit?

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SUMMARY

The limit of the ratio of Bessel functions, specifically $$\lim_{x \to 0} [ \frac{J_{p}(x)}{Y_{p}(x)} ]$$, is determined to be 0 when approaching along the positive real axis for integer values of p. The singularity at x=0 in the function Y_p(x) influences the limit's behavior, necessitating careful consideration of the approach path. This conclusion is established based on the properties of Bessel functions and their asymptotic behavior near singular points.

PREREQUISITES
  • Understanding of Bessel functions, specifically J_p(x) and Y_p(x)
  • Knowledge of limits and singular points in calculus
  • Familiarity with asymptotic analysis
  • Basic proficiency in mathematical notation and expressions
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  • Study the properties of Bessel functions, focusing on J_p(x) and Y_p(x)
  • Explore techniques for evaluating limits involving singular points
  • Learn about asymptotic expansions of Bessel functions
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Mathematicians, physics students, and researchers dealing with differential equations and special functions, particularly those interested in the behavior of Bessel functions near singularities.

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TL;DR
I got to calculate this limit, but It is not clear to me if I have to use the original defitinion from the Bessels terms because I have already tried and It didn't resulted.
If you could suggest me a way to do it you would help me a lot.
Thanks
$$
\lim_{x \to 0} [ \frac{J_{p}(x)}{Y_{p}(x)} ]
$$
 
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The problem I see is ##x=0## is a singular point of ##Y_p(x)## so the answer will depend on how one approaches ##x=0##. for ##p## an integer and approaching along the real ##+x## axis I think the limit is 0.
 
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