Expansion of trignometric function around infinity
I need to expand $cos[sqrt{x^2+a^2+b x}]$ around $x=infty$ and want to keep terms only upto $x^{-3}$. Here $a$ and $b$ are constant. Should I first expand the function $sqrt{(x^2+a^2+b x)}$ and then write the usual cosine series? Is this the right way to approach this question? If not then what should be the right approach. Thanks
calculus real-analysis mathematical-physics
asked Nov 20 at 15:38
Parveen
275
add a comment |
I need to expand $cos[sqrt{x^2+a^2+b x}]$ around $x=infty$ and want to keep terms only upto $x^{-3}$. Here $a$ and $b$ are constant. Should I first expand the function $sqrt{(x^2+a^2+b x)}$ and then write the usual cosine series? Is this the right way to approach this question? If not then what should be the right approach. Thanks
calculus real-analysis mathematical-physics
asked Nov 20 at 15:38
Parveen
275
Why do you think that such an expansion exists?
– gammatester
Nov 20 at 15:45
What does $theta$ has to do with $x$? You can just use $2picostheta$ as a constant, say $c$.
– Andrei
Nov 20 at 16:12
@Andrei: True, you can do that. $theta$ is a constant.
– Parveen
Nov 20 at 19:17
@gammatester: I don't really know if it exist. Can you show that it doesn't exist?
– Parveen
Nov 20 at 19:18
2
$cos$ has an essential singularity at $infty$
– gammatester
Nov 20 at 19:44
add a comment |
I need to expand $cos[sqrt{x^2+a^2+b x}]$ around $x=infty$ and want to keep terms only upto $x^{-3}$. Here $a$ and $b$ are constant. Should I first expand the function $sqrt{(x^2+a^2+b x)}$ and then write the usual cosine series? Is this the right way to approach this question? If not then what should be the right approach. Thanks
calculus real-analysis mathematical-physics
asked Nov 20 at 15:38
Parveen
275
I need to expand $cos[sqrt{x^2+a^2+b x}]$ around $x=infty$ and want to keep terms only upto $x^{-3}$. Here $a$ and $b$ are constant. Should I first expand the function $sqrt{(x^2+a^2+b x)}$ and then write the usual cosine series? Is this the right way to approach this question? If not then what should be the right approach. Thanks
calculus real-analysis mathematical-physics
calculus real-analysis mathematical-physics
asked Nov 20 at 15:38
Parveen
275
asked Nov 20 at 15:38
Parveen
275
edited Nov 20 at 19:24
asked Nov 20 at 15:38
Parveen
275
asked Nov 20 at 15:38
Parveen
275
asked Nov 20 at 15:38
Parveen
275
275
Why do you think that such an expansion exists?
– gammatester
Nov 20 at 15:45
What does $theta$ has to do with $x$? You can just use $2picostheta$ as a constant, say $c$.
– Andrei
Nov 20 at 16:12
@Andrei: True, you can do that. $theta$ is a constant.
– Parveen
Nov 20 at 19:17
@gammatester: I don't really know if it exist. Can you show that it doesn't exist?
– Parveen
Nov 20 at 19:18
2
$cos$ has an essential singularity at $infty$
– gammatester
Nov 20 at 19:44
add a comment |
Why do you think that such an expansion exists?
– gammatester
Nov 20 at 15:45
What does $theta$ has to do with $x$? You can just use $2picostheta$ as a constant, say $c$.
– Andrei
Nov 20 at 16:12
@Andrei: True, you can do that. $theta$ is a constant.
– Parveen
Nov 20 at 19:17
@gammatester: I don't really know if it exist. Can you show that it doesn't exist?
– Parveen
Nov 20 at 19:18
2
$cos$ has an essential singularity at $infty$
– gammatester
Nov 20 at 19:44
Why do you think that such an expansion exists?
– gammatester
Nov 20 at 15:45
Why do you think that such an expansion exists?
– gammatester
Nov 20 at 15:45
What does $theta$ has to do with $x$? You can just use $2picostheta$ as a constant, say $c$.
– Andrei
Nov 20 at 16:12
What does $theta$ has to do with $x$? You can just use $2picostheta$ as a constant, say $c$.
– Andrei
Nov 20 at 16:12
@Andrei: True, you can do that. $theta$ is a constant.
– Parveen
Nov 20 at 19:17
@Andrei: True, you can do that. $theta$ is a constant.
– Parveen
Nov 20 at 19:17
@gammatester: I don't really know if it exist. Can you show that it doesn't exist?
– Parveen
Nov 20 at 19:18
@gammatester: I don't really know if it exist. Can you show that it doesn't exist?
– Parveen
Nov 20 at 19:18
2
2
$cos$ has an essential singularity at $infty$
– gammatester
Nov 20 at 19:44
$cos$ has an essential singularity at $infty$
– gammatester
Nov 20 at 19:44
add a comment |
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Why do you think that such an expansion exists?
– gammatester
Nov 20 at 15:45
What does $theta$ has to do with $x$? You can just use $2picostheta$ as a constant, say $c$.
– Andrei
Nov 20 at 16:12
@Andrei: True, you can do that. $theta$ is a constant.
– Parveen
Nov 20 at 19:17
@gammatester: I don't really know if it exist. Can you show that it doesn't exist?
– Parveen
Nov 20 at 19:18
2
$cos$ has an essential singularity at $infty$
– gammatester
Nov 20 at 19:44