Domain of the Bessel Function

  • #1
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Homework Statement


Find domain of [tex]\sum_{n= 0}^\infty \frac{(-1)^{n}x^{2n}}{2^{2n}(n!)^{2}}[/tex]


Homework Equations




The Attempt at a Solution


I set it all up but I can't really seem to simplify it.

[tex]\frac{(-1)^{n+1}x^{2(n+1)}}{2^{2n+2}(n+1)!^{2}}\bullet\frac{2^{2n}(n!)^{2}}{(-1)^{n}x^{2n}} [/tex]
 

Answers and Replies

  • #2
Dick
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Why can't you simplify it? What's 2^(2n)/(2^(2n+2))? What's n!/(n+1)!?
 
  • #3
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You mean polynomial division?
 
  • #4
Dick
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You mean polynomial division?

No, I mean the law of exponents for the first one and realizing (n)!/(n+1)!=(1*2*3*...*n)/(1*2*3*...*n*(n+1)) for the second one.
 
  • #5
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Explain what the mean by showing me on this much simpler one.

[tex]\sum_{n= 0}^\infty n!x^{n}[/tex]

Setting it up I get [tex]\frac{(1+n!)x^{n+1}}{n!x^{n}}[/tex]

Do I cross out the factors?
 
  • #6
Dick
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You meant to write (1+n)!, I hope, not (1+n!). Yes, you just cancel the common factors in the numerator and denominator. What do you get?
 
  • #7
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So, I got x+1 but I must have messed something up.
 
  • #8
Dick
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So, I got x+1 but I must have messed something up.

Apparently, but not showing how you got that doesn't make it easy to help. What are x^(n+1)/x^n and (n+1)!/n!?????
 

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