Is there any hope with this integral?
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I can't figure out how to take this integral. Looks pretty standard to me, but somehow can't find anything helpful in the literature:
$int_0^{2pi} dphi; (1-2 a cos phi + a^2)^{k+ (kappa/2)} e^{-i( ell - kappa) phi} $
MMA is stuck with it as well, which makes me suspicious if the closed form exists...
Any help with this is highly appreciated!
integration definite-integrals exponential-function
asked Dec 13 '18 at 17:57
MsTaisMsTais
1808
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add a comment |
$begingroup$
I can't figure out how to take this integral. Looks pretty standard to me, but somehow can't find anything helpful in the literature:
$int_0^{2pi} dphi; (1-2 a cos phi + a^2)^{k+ (kappa/2)} e^{-i( ell - kappa) phi} $
MMA is stuck with it as well, which makes me suspicious if the closed form exists...
Any help with this is highly appreciated!
integration definite-integrals exponential-function
asked Dec 13 '18 at 17:57
MsTaisMsTais
1808
$endgroup$
$begingroup$
One can write $1-2a cosphi+a^2=(a-e^{i phi})(a-e^{-i phi})=|a-e^{i phi}|^2$ ; I would then try integration by residues.
$endgroup$
– Jean Marie
Dec 13 '18 at 18:08
$begingroup$
@Jean Marie Thank you for the idea! I'll try it out.
$endgroup$
– MsTais
Dec 13 '18 at 18:36
add a comment |
$begingroup$
I can't figure out how to take this integral. Looks pretty standard to me, but somehow can't find anything helpful in the literature:
$int_0^{2pi} dphi; (1-2 a cos phi + a^2)^{k+ (kappa/2)} e^{-i( ell - kappa) phi} $
MMA is stuck with it as well, which makes me suspicious if the closed form exists...
Any help with this is highly appreciated!
integration definite-integrals exponential-function
asked Dec 13 '18 at 17:57
MsTaisMsTais
1808
$endgroup$
I can't figure out how to take this integral. Looks pretty standard to me, but somehow can't find anything helpful in the literature:
$int_0^{2pi} dphi; (1-2 a cos phi + a^2)^{k+ (kappa/2)} e^{-i( ell - kappa) phi} $
MMA is stuck with it as well, which makes me suspicious if the closed form exists...
Any help with this is highly appreciated!
integration definite-integrals exponential-function
integration definite-integrals exponential-function
asked Dec 13 '18 at 17:57
MsTaisMsTais
1808
asked Dec 13 '18 at 17:57
MsTaisMsTais
1808
asked Dec 13 '18 at 17:57
MsTaisMsTais
1808
asked Dec 13 '18 at 17:57
MsTaisMsTais
1808
asked Dec 13 '18 at 17:57
MsTaisMsTais
1808
1808
$begingroup$
One can write $1-2a cosphi+a^2=(a-e^{i phi})(a-e^{-i phi})=|a-e^{i phi}|^2$ ; I would then try integration by residues.
$endgroup$
– Jean Marie
Dec 13 '18 at 18:08
$begingroup$
@Jean Marie Thank you for the idea! I'll try it out.
$endgroup$
– MsTais
Dec 13 '18 at 18:36
add a comment |
$begingroup$
One can write $1-2a cosphi+a^2=(a-e^{i phi})(a-e^{-i phi})=|a-e^{i phi}|^2$ ; I would then try integration by residues.
$endgroup$
– Jean Marie
Dec 13 '18 at 18:08
$begingroup$
@Jean Marie Thank you for the idea! I'll try it out.
$endgroup$
– MsTais
Dec 13 '18 at 18:36
$begingroup$
One can write $1-2a cosphi+a^2=(a-e^{i phi})(a-e^{-i phi})=|a-e^{i phi}|^2$ ; I would then try integration by residues.
$endgroup$
– Jean Marie
Dec 13 '18 at 18:08
$begingroup$
One can write $1-2a cosphi+a^2=(a-e^{i phi})(a-e^{-i phi})=|a-e^{i phi}|^2$ ; I would then try integration by residues.
$endgroup$
– Jean Marie
Dec 13 '18 at 18:08
$begingroup$
@Jean Marie Thank you for the idea! I'll try it out.
$endgroup$
– MsTais
Dec 13 '18 at 18:36
$begingroup$
@Jean Marie Thank you for the idea! I'll try it out.
$endgroup$
– MsTais
Dec 13 '18 at 18:36
add a comment |
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$begingroup$
One can write $1-2a cosphi+a^2=(a-e^{i phi})(a-e^{-i phi})=|a-e^{i phi}|^2$ ; I would then try integration by residues.
$endgroup$
– Jean Marie
Dec 13 '18 at 18:08
$begingroup$
@Jean Marie Thank you for the idea! I'll try it out.
$endgroup$
– MsTais
Dec 13 '18 at 18:36