Analytic form of the infinite integration with oscillatory integrand?
I recently have a problem as follows
$int_0^infty cos bigl[ { k cdot t over {sqrt{1 + k^2}} } bigr] cdot cos bigl[ k cdot x bigr] , dk$
Here, x and t are spatial and temporal constant. I’m trying to find the analytic form for the root. I’ve tried to (and considered) find it via complex analysis(Residue theorem), Riemann–Lebesgue lemma, integration table, quadratures, etc…, however, it failed.
Thank you for your advice for comments for that and the answers in advance.
Many thanks indeed.
improper-integrals oscillatory-integral
asked Dec 26 at 5:57
Jinsoo Park
111
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add a comment |
I recently have a problem as follows
$int_0^infty cos bigl[ { k cdot t over {sqrt{1 + k^2}} } bigr] cdot cos bigl[ k cdot x bigr] , dk$
Here, x and t are spatial and temporal constant. I’m trying to find the analytic form for the root. I’ve tried to (and considered) find it via complex analysis(Residue theorem), Riemann–Lebesgue lemma, integration table, quadratures, etc…, however, it failed.
Thank you for your advice for comments for that and the answers in advance.
Many thanks indeed.
improper-integrals oscillatory-integral
asked Dec 26 at 5:57
Jinsoo Park
111
New contributor
Jinsoo Park is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Integral is divergent.
– Mariusz Iwaniuk
Dec 26 at 10:19
add a comment |
I recently have a problem as follows
$int_0^infty cos bigl[ { k cdot t over {sqrt{1 + k^2}} } bigr] cdot cos bigl[ k cdot x bigr] , dk$
Here, x and t are spatial and temporal constant. I’m trying to find the analytic form for the root. I’ve tried to (and considered) find it via complex analysis(Residue theorem), Riemann–Lebesgue lemma, integration table, quadratures, etc…, however, it failed.
Thank you for your advice for comments for that and the answers in advance.
Many thanks indeed.
improper-integrals oscillatory-integral
asked Dec 26 at 5:57
Jinsoo Park
111
New contributor
Jinsoo Park is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I recently have a problem as follows
$int_0^infty cos bigl[ { k cdot t over {sqrt{1 + k^2}} } bigr] cdot cos bigl[ k cdot x bigr] , dk$
Here, x and t are spatial and temporal constant. I’m trying to find the analytic form for the root. I’ve tried to (and considered) find it via complex analysis(Residue theorem), Riemann–Lebesgue lemma, integration table, quadratures, etc…, however, it failed.
Thank you for your advice for comments for that and the answers in advance.
Many thanks indeed.
improper-integrals oscillatory-integral
improper-integrals oscillatory-integral
asked Dec 26 at 5:57
Jinsoo Park
111
New contributor
Jinsoo Park is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 26 at 5:57
Jinsoo Park
111
New contributor
Jinsoo Park is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 26 at 5:57
Jinsoo Park
111
New contributor
Jinsoo Park is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Dec 26 at 5:57
Jinsoo Park
111
asked Dec 26 at 5:57
Jinsoo Park
111
111
New contributor
Jinsoo Park is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Jinsoo Park is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Jinsoo Park is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Integral is divergent.
– Mariusz Iwaniuk
Dec 26 at 10:19
add a comment |
Integral is divergent.
– Mariusz Iwaniuk
Dec 26 at 10:19
Integral is divergent.
– Mariusz Iwaniuk
Dec 26 at 10:19
Integral is divergent.
– Mariusz Iwaniuk
Dec 26 at 10:19
add a comment |
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Integral is divergent.
– Mariusz Iwaniuk
Dec 26 at 10:19