Bessel FUnction small arguments

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SUMMARY

The discussion focuses on approximations for Bessel functions J_n with small arguments. Matt suggests using WolframAlpha to enter "J(n,x)" for quick calculations and references the Taylor Series expansion around x=0. He recommends the book "Handbook of Mathematical Functions" by Abramowitz and Stegun as a primary resource for special function properties, specifically pointing to the chapter on Bessel functions of integer order available online.

PREREQUISITES
  • Understanding of Bessel functions, specifically J_n
  • Familiarity with Taylor Series expansions
  • Basic knowledge of mathematical functions and their properties
  • Access to online mathematical resources like WolframAlpha
NEXT STEPS
  • Explore the Taylor Series expansion for Bessel functions J_n
  • Utilize WolframAlpha for calculating Bessel functions with small arguments
  • Read the chapter on Bessel functions in Abramowitz and Stegun's "Handbook of Mathematical Functions"
  • Investigate other special functions and their approximations
USEFUL FOR

Mathematicians, physicists, engineers, and anyone involved in computational mathematics or needing to work with Bessel functions and their approximations.

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What are the approximations for Bessel functions J_n with small arguments? I've had a very hard time finding this online.

Thanks!
-Matt
 
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May want to try WolframAlpha cite http://www.wolframalpha.com/"

Enter "J(n,x)"

and see Taylor Series about x=0
 
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Abramowitz and Stegun is my first go-to source for special function properties. It is available online! The chapter on Bessel functions of integer order can be found at:

http://www.math.ucla.edu/~cbm/aands//page_355.htm

enjoy
 
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