anonymous
  • anonymous
Meta-math \[\int_{0}^{\infty} \text{J}_0(a\sqrt{1+x^2}) \ \text{d}x\]
Meta-math
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
What is J_o
anonymous
  • anonymous
@mukushla can u PLZ explain me the symbols?
anonymous
  • anonymous
\(J_0\) is the bessel function of order 0

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experimentX
  • experimentX
looks like you are up to something!!
experimentX
  • experimentX
\[ J_\alpha(x) = \sum_{m=0}^\infty \frac{(-1)^m}{m! \, \Gamma(m+\alpha+1)} {\left(\tfrac{1}{2}x\right)}^{2m+\alpha} \] \[ \int_0^\infty \sum_{m=0}^\infty \frac{(-1)^m}{m! \, \Gamma(m+1)}\left( {1 \over 2} a \sqrt{ 1 + x^2}\right)^{2m} \\ \]
experimentX
  • experimentX
|dw:1349011854953:dw|
experimentX
  • experimentX
this doesn't looks like converging ... let's try some other.
experimentX
  • experimentX
For a=1, the numerical value seems to be 0.540302
anonymous
  • anonymous
\[\int_{0}^{\infty} \text{J}_0(a\sqrt{1+x^2}) \ \text{d}x=\frac{\cos a}{a}\]
experimentX
  • experimentX
how do do that man?
anonymous
  • anonymous
using the formula\[\large J_\lambda(z)=\frac{1}{2\pi i}(\frac{z}{2})^{\lambda} \int_C t^{-\lambda+1} e^{t-\frac{z^2}{4t}} \text{d}t\]

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