An closed-form expression of an integral of Chebyshev series and exponential function
up vote
2
down vote
favorite
Does the following integral has a closed-form expression?
$int_{-1}^{1} T_n(x)exp(ipi x)dx,$
where, $T_n$ is the Chebyshev polynomial of degree n.
integration polynomials orthogonal-polynomials
asked Nov 16 at 20:52
Ray
767
add a comment |
up vote
2
down vote
favorite
Does the following integral has a closed-form expression?
$int_{-1}^{1} T_n(x)exp(ipi x)dx,$
where, $T_n$ is the Chebyshev polynomial of degree n.
integration polynomials orthogonal-polynomials
asked Nov 16 at 20:52
Ray
767
Have you tried using the explicit form $T_n(x)=cos (n arccos x)$? Maybe some Bessel functions would appear?
– Yuriy S
Nov 16 at 21:08
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Does the following integral has a closed-form expression?
$int_{-1}^{1} T_n(x)exp(ipi x)dx,$
where, $T_n$ is the Chebyshev polynomial of degree n.
integration polynomials orthogonal-polynomials
asked Nov 16 at 20:52
Ray
767
Does the following integral has a closed-form expression?
$int_{-1}^{1} T_n(x)exp(ipi x)dx,$
where, $T_n$ is the Chebyshev polynomial of degree n.
integration polynomials orthogonal-polynomials
integration polynomials orthogonal-polynomials
asked Nov 16 at 20:52
Ray
767
asked Nov 16 at 20:52
Ray
767
asked Nov 16 at 20:52
Ray
767
asked Nov 16 at 20:52
Ray
767
asked Nov 16 at 20:52
Ray
767
767
Have you tried using the explicit form $T_n(x)=cos (n arccos x)$? Maybe some Bessel functions would appear?
– Yuriy S
Nov 16 at 21:08
add a comment |
Have you tried using the explicit form $T_n(x)=cos (n arccos x)$? Maybe some Bessel functions would appear?
– Yuriy S
Nov 16 at 21:08
Have you tried using the explicit form $T_n(x)=cos (n arccos x)$? Maybe some Bessel functions would appear?
– Yuriy S
Nov 16 at 21:08
Have you tried using the explicit form $T_n(x)=cos (n arccos x)$? Maybe some Bessel functions would appear?
– Yuriy S
Nov 16 at 21:08
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%2f3001630%2fan-closed-form-expression-of-an-integral-of-chebyshev-series-and-exponential-fun%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
Have you tried using the explicit form $T_n(x)=cos (n arccos x)$? Maybe some Bessel functions would appear?
– Yuriy S
Nov 16 at 21:08