- #1
Monsterman222
- 11
- 0
I am aware that Bessel functions of any order [itex]p[/itex] are zero in the limit where x approaches infinity. From the formula of Bessel functions, I can't see why this is. The formula is:
[tex]J_p\left(x\right)=\sum_{n=0}^{\infty} \frac{\left(-1\right)^n}{\Gamma\left(n+1\right)\Gamma\left(n+1+p\right)}\left(\frac{x}{2}\right)^{2n+p}[/tex]
Does anyone know a proof of why this is? That is, why is it that
[tex]\lim_{x\to\infty}J_p\left(x\right)=0[/tex]
[tex]J_p\left(x\right)=\sum_{n=0}^{\infty} \frac{\left(-1\right)^n}{\Gamma\left(n+1\right)\Gamma\left(n+1+p\right)}\left(\frac{x}{2}\right)^{2n+p}[/tex]
Does anyone know a proof of why this is? That is, why is it that
[tex]\lim_{x\to\infty}J_p\left(x\right)=0[/tex]