asymptotic expansion of integral of Bessel function?
up vote
1
down vote
favorite
The integral is
$$int_0^infty dxfrac{x J_1(sqrt{y} cdot x/pi)^2}{ysinh^2(x)}$$
I want to compute it in large $y$ expansion. I have checked numerically that the integral is convergent for all positive $y$. Numerically, the leading term seems to be $frac{1}{2y}$, i would like to compute at least the next few terms.
definite-integrals asymptotics
edited Nov 17 at 21:51
Yuriy S
15.3k433115
asked Sep 13 at 0:55
esches
212
add a comment |
up vote
1
down vote
favorite
The integral is
$$int_0^infty dxfrac{x J_1(sqrt{y} cdot x/pi)^2}{ysinh^2(x)}$$
I want to compute it in large $y$ expansion. I have checked numerically that the integral is convergent for all positive $y$. Numerically, the leading term seems to be $frac{1}{2y}$, i would like to compute at least the next few terms.
definite-integrals asymptotics
edited Nov 17 at 21:51
Yuriy S
15.3k433115
asked Sep 13 at 0:55
esches
212
The same question has an answer here. (Just change $y$ into $sqrt{y}/pi$ and divide the result by $y$).
– Paul Enta
Nov 17 at 22:59
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
The integral is
$$int_0^infty dxfrac{x J_1(sqrt{y} cdot x/pi)^2}{ysinh^2(x)}$$
I want to compute it in large $y$ expansion. I have checked numerically that the integral is convergent for all positive $y$. Numerically, the leading term seems to be $frac{1}{2y}$, i would like to compute at least the next few terms.
definite-integrals asymptotics
edited Nov 17 at 21:51
Yuriy S
15.3k433115
asked Sep 13 at 0:55
esches
212
The integral is
$$int_0^infty dxfrac{x J_1(sqrt{y} cdot x/pi)^2}{ysinh^2(x)}$$
I want to compute it in large $y$ expansion. I have checked numerically that the integral is convergent for all positive $y$. Numerically, the leading term seems to be $frac{1}{2y}$, i would like to compute at least the next few terms.
definite-integrals asymptotics
definite-integrals asymptotics
edited Nov 17 at 21:51
Yuriy S
15.3k433115
asked Sep 13 at 0:55
esches
212
edited Nov 17 at 21:51
Yuriy S
15.3k433115
asked Sep 13 at 0:55
esches
212
edited Nov 17 at 21:51
Yuriy S
15.3k433115
edited Nov 17 at 21:51
Yuriy S
15.3k433115
edited Nov 17 at 21:51
Yuriy S
15.3k433115
15.3k433115
asked Sep 13 at 0:55
esches
212
asked Sep 13 at 0:55
esches
212
asked Sep 13 at 0:55
esches
212
212
The same question has an answer here. (Just change $y$ into $sqrt{y}/pi$ and divide the result by $y$).
– Paul Enta
Nov 17 at 22:59
add a comment |
The same question has an answer here. (Just change $y$ into $sqrt{y}/pi$ and divide the result by $y$).
– Paul Enta
Nov 17 at 22:59
The same question has an answer here. (Just change $y$ into $sqrt{y}/pi$ and divide the result by $y$).
– Paul Enta
Nov 17 at 22:59
The same question has an answer here. (Just change $y$ into $sqrt{y}/pi$ and divide the result by $y$).
– Paul Enta
Nov 17 at 22:59
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2915009%2fasymptotic-expansion-of-integral-of-bessel-function%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
The same question has an answer here. (Just change $y$ into $sqrt{y}/pi$ and divide the result by $y$).
– Paul Enta
Nov 17 at 22:59