Is a Mac donald function really a Bessel function

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SUMMARY

A Macdonald function is indeed a type of modified Bessel function of the second kind, specifically represented as J_{a}(ix) = CK_{a}(x), where 'C' is a complex constant. The discussion clarifies that Macdonald functions are synonymous with Bessel functions of the third kind, also known as Basset functions or modified Hankel functions. This relationship highlights the interconnectedness of these mathematical functions and their applications in various fields.

PREREQUISITES
  • Understanding of Bessel functions, specifically modified Bessel functions of the second kind.
  • Familiarity with complex numbers and their properties.
  • Knowledge of mathematical function notation and terminology.
  • Basic understanding of special functions in mathematical analysis.
NEXT STEPS
  • Research the properties and applications of modified Bessel functions of the second kind.
  • Explore the relationship between Macdonald functions and Basset functions.
  • Study the implications of complex arguments in Bessel functions.
  • Learn about the applications of modified Hankel functions in physics and engineering.
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Mathematicians, physicists, and engineers interested in special functions, particularly those working with Bessel functions and their applications in theoretical and applied contexts.

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my question is if a Mac Donald function is really a Bessel function i mean

J_{a}(ix)= CK_{a}(x)

here 'C' is a complex number
 
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As far as I know a Mac Donald function is the same as a modified Bessel function of the second kind
 
The modified Bessel functions of the second kind of imaginary argument (or the Bessel functions of the third kind) are alternatively named Basset functions , Macdonald functions, or modified Hankel functions.
 

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