Derivation of bessel generating function

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SUMMARY

The Bessel generating function is defined as exp(x*(t-(1/t))/2) = Σ from n=0 to ∞ (Jn(x)t^n). The discussion highlights the use of the McLaurin expansion of exponentials to manipulate the left-hand side of the equation. Participants seek clarity on equating powers to match the right-hand side and inquire about typing mathematical symbols without LaTeX. A resource link was provided for typing symbols effectively.

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  • Understanding of Bessel functions, specifically Jn(x)
  • Familiarity with exponential functions and their properties
  • Knowledge of McLaurin series expansion
  • Basic skills in typing mathematical symbols and notation
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  • Study the properties and applications of Bessel functions in mathematical physics
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Students and educators in mathematics, particularly those focused on special functions, as well as anyone interested in mathematical notation and typesetting without LaTeX.

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Homework Statement


The bessel generating function:
exp(x*(t-(1/t))/2)=sum from 0 to n(Jn(x)t^(n))

Homework Equations





The Attempt at a Solution


exp(x*(t-(1/t))/2)=exp((x/2)*t)exp((x/2)*(1/t))
used the McLaurin expansion of exponentials. Not sure how to bring the powers equal to that of the right hand side.
How could I type symbols wthout using latex.

Thanx
 
Physics news on Phys.org
To type symbols without using latex: Look at this https://www.physicsforums.com/blog.php?b=347" from Redbelly98.
 
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