Zero's of the modified Bessel functions,

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SUMMARY

The discussion focuses on determining the zeros of the modified Bessel functions of the first and second kind, specifically in the context of solving Airy's differential equation using Airy functions, Ai(x) and Bi(x). The solution requires fitting these functions to boundary conditions that necessitate a zero value at the boundary. The referenced paper provides additional insights into the zeros of these modified Bessel functions, which are crucial for achieving the desired solution.

PREREQUISITES
  • Understanding of Airy functions, Ai(x) and Bi(x)
  • Knowledge of modified Bessel functions of the first and second kind
  • Familiarity with differential equations, particularly Airy's differential equation
  • Ability to apply boundary conditions in mathematical solutions
NEXT STEPS
  • Research the properties and applications of modified Bessel functions of the first and second kind
  • Study the methods for solving Airy's differential equation
  • Examine the paper on zeros of modified Bessel functions for detailed mathematical insights
  • Explore numerical methods for finding zeros of special functions
USEFUL FOR

Mathematicians, physicists, and engineers working on differential equations, particularly those involving Airy functions and modified Bessel functions, will benefit from this discussion.

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I have the solution to a particular D.E. (Airy's D.E.) which is in terms of Airy functions, namely a linear combination of Ai(x) and Bi(x), to which I have to fit to the boundary conditions. Both Ai(x) and Bi(x) can be cast into a form which involves both modified Bessel functions of the first and second kind. The bondary conditions are such that the solution must be zero at the boundary. Therefore my question is this,

What are the zero's of the modified Bessel functions of the first and second kind?
 
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