Solving Naumann Equation: How Bessel's Second Kind Was Discovered

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SUMMARY

The discussion centers on the derivation of Bessel's second kind functions as solutions to the Bessel differential equation, particularly focusing on the contributions of Naumann. The Bessel functions of the second kind are specifically noted for their singular behavior at the origin. For a comprehensive proof and further details, participants are directed to the resource available at MathWorld.

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  • Bessel differential equations
  • Bessel functions of the first and second kind
  • Mathematical proof techniques
  • Understanding of singularities in differential equations
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  • Study the derivation of Bessel functions of the first kind
  • Explore the properties of Bessel functions of the second kind
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Mathematicians, physicists, and engineering students interested in advanced mathematical functions and their applications in solving differential equations.

Aleen Muhammed
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How Naumann arrived to the second kind of Bessel ?

I want proof , Please ..

http://C:\Users\User\Downloads
 
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Aleen Muhammed said:
How Naumann arrived to the second kind of Bessel ?

these functions are solution to the Bessel differential equation which is singular at the origin.
for a proof you can see
<http://mathworld.wolfram.com/BesselFunctionoftheSecondKind.html>
 
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