Evaluation of integrals
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I wast to evaluate the following integrals:
begin{multline} label{eqlens12}
int_0^{infty}frac{(1+4lambda^2)}{(1+lambda^2)left[lambdasin(2eta_2)+sinh(2lambdaeta_2)right]} \
left{lambdasin(2eta_2)+sinh(2lambdaeta_2)+left[1+2lambda^2sin^2eta_2-cosh(2lambdaeta_2)right]tanh(lambdapi)right},dlambda.
end{multline}
begin{equation} label{eqlens11}
int_0^{infty}frac{(1+4lambda^2)left{1+(1+2lambda^2)left[3cosh(lambdapi)-cosh(3lambdapi)right]
-3cosh(2lambdapi)right},dlambda}{2(1+lambda^2)cosh(lambdapi)left[1+2lambda^2-cosh(3lambdapi)right]}.
end{equation}
begin{equation}
int_0^{infty}(4lambda^2+1)left[1-tanh(lambdaeta_2)tanh(lambdapi)right],dlambda.
end{equation}
In the first and last integrals $pi>eta_2>0$. Would be grateful if anybody can help.
integration
asked Dec 14 '18 at 9:22
JogJog
64
$endgroup$
add a comment |
$begingroup$
I wast to evaluate the following integrals:
begin{multline} label{eqlens12}
int_0^{infty}frac{(1+4lambda^2)}{(1+lambda^2)left[lambdasin(2eta_2)+sinh(2lambdaeta_2)right]} \
left{lambdasin(2eta_2)+sinh(2lambdaeta_2)+left[1+2lambda^2sin^2eta_2-cosh(2lambdaeta_2)right]tanh(lambdapi)right},dlambda.
end{multline}
begin{equation} label{eqlens11}
int_0^{infty}frac{(1+4lambda^2)left{1+(1+2lambda^2)left[3cosh(lambdapi)-cosh(3lambdapi)right]
-3cosh(2lambdapi)right},dlambda}{2(1+lambda^2)cosh(lambdapi)left[1+2lambda^2-cosh(3lambdapi)right]}.
end{equation}
begin{equation}
int_0^{infty}(4lambda^2+1)left[1-tanh(lambdaeta_2)tanh(lambdapi)right],dlambda.
end{equation}
In the first and last integrals $pi>eta_2>0$. Would be grateful if anybody can help.
integration
asked Dec 14 '18 at 9:22
JogJog
64
$endgroup$
$begingroup$
Have you tried with WolframAlpha?
$endgroup$
– Nosrati
Dec 14 '18 at 12:53
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Yes, of course. It is able to evaluate the integrals for special values of $eta_2$ (especially in the last integral, it is able to evaluate for $eta_2=pi/4,pi/2,pi$ etc. (the upper limit for $eta_2$ should $le pi$ and not $<pi$), but I am not able to find the general expression from these particular cases.
$endgroup$
– Jog
Dec 15 '18 at 3:31
add a comment |
$begingroup$
I wast to evaluate the following integrals:
begin{multline} label{eqlens12}
int_0^{infty}frac{(1+4lambda^2)}{(1+lambda^2)left[lambdasin(2eta_2)+sinh(2lambdaeta_2)right]} \
left{lambdasin(2eta_2)+sinh(2lambdaeta_2)+left[1+2lambda^2sin^2eta_2-cosh(2lambdaeta_2)right]tanh(lambdapi)right},dlambda.
end{multline}
begin{equation} label{eqlens11}
int_0^{infty}frac{(1+4lambda^2)left{1+(1+2lambda^2)left[3cosh(lambdapi)-cosh(3lambdapi)right]
-3cosh(2lambdapi)right},dlambda}{2(1+lambda^2)cosh(lambdapi)left[1+2lambda^2-cosh(3lambdapi)right]}.
end{equation}
begin{equation}
int_0^{infty}(4lambda^2+1)left[1-tanh(lambdaeta_2)tanh(lambdapi)right],dlambda.
end{equation}
In the first and last integrals $pi>eta_2>0$. Would be grateful if anybody can help.
integration
asked Dec 14 '18 at 9:22
JogJog
64
$endgroup$
I wast to evaluate the following integrals:
begin{multline} label{eqlens12}
int_0^{infty}frac{(1+4lambda^2)}{(1+lambda^2)left[lambdasin(2eta_2)+sinh(2lambdaeta_2)right]} \
left{lambdasin(2eta_2)+sinh(2lambdaeta_2)+left[1+2lambda^2sin^2eta_2-cosh(2lambdaeta_2)right]tanh(lambdapi)right},dlambda.
end{multline}
begin{equation} label{eqlens11}
int_0^{infty}frac{(1+4lambda^2)left{1+(1+2lambda^2)left[3cosh(lambdapi)-cosh(3lambdapi)right]
-3cosh(2lambdapi)right},dlambda}{2(1+lambda^2)cosh(lambdapi)left[1+2lambda^2-cosh(3lambdapi)right]}.
end{equation}
begin{equation}
int_0^{infty}(4lambda^2+1)left[1-tanh(lambdaeta_2)tanh(lambdapi)right],dlambda.
end{equation}
In the first and last integrals $pi>eta_2>0$. Would be grateful if anybody can help.
integration
integration
asked Dec 14 '18 at 9:22
JogJog
64
asked Dec 14 '18 at 9:22
JogJog
64
asked Dec 14 '18 at 9:22
JogJog
64
asked Dec 14 '18 at 9:22
JogJog
64
asked Dec 14 '18 at 9:22
JogJog
64
64
$begingroup$
Have you tried with WolframAlpha?
$endgroup$
– Nosrati
Dec 14 '18 at 12:53
$begingroup$
Yes, of course. It is able to evaluate the integrals for special values of $eta_2$ (especially in the last integral, it is able to evaluate for $eta_2=pi/4,pi/2,pi$ etc. (the upper limit for $eta_2$ should $le pi$ and not $<pi$), but I am not able to find the general expression from these particular cases.
$endgroup$
– Jog
Dec 15 '18 at 3:31
add a comment |
$begingroup$
Have you tried with WolframAlpha?
$endgroup$
– Nosrati
Dec 14 '18 at 12:53
$begingroup$
Yes, of course. It is able to evaluate the integrals for special values of $eta_2$ (especially in the last integral, it is able to evaluate for $eta_2=pi/4,pi/2,pi$ etc. (the upper limit for $eta_2$ should $le pi$ and not $<pi$), but I am not able to find the general expression from these particular cases.
$endgroup$
– Jog
Dec 15 '18 at 3:31
$begingroup$
Have you tried with WolframAlpha?
$endgroup$
– Nosrati
Dec 14 '18 at 12:53
$begingroup$
Have you tried with WolframAlpha?
$endgroup$
– Nosrati
Dec 14 '18 at 12:53
$begingroup$
Yes, of course. It is able to evaluate the integrals for special values of $eta_2$ (especially in the last integral, it is able to evaluate for $eta_2=pi/4,pi/2,pi$ etc. (the upper limit for $eta_2$ should $le pi$ and not $<pi$), but I am not able to find the general expression from these particular cases.
$endgroup$
– Jog
Dec 15 '18 at 3:31
$begingroup$
Yes, of course. It is able to evaluate the integrals for special values of $eta_2$ (especially in the last integral, it is able to evaluate for $eta_2=pi/4,pi/2,pi$ etc. (the upper limit for $eta_2$ should $le pi$ and not $<pi$), but I am not able to find the general expression from these particular cases.
$endgroup$
– Jog
Dec 15 '18 at 3:31
add a comment |
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$begingroup$
Have you tried with WolframAlpha?
$endgroup$
– Nosrati
Dec 14 '18 at 12:53
$begingroup$
Yes, of course. It is able to evaluate the integrals for special values of $eta_2$ (especially in the last integral, it is able to evaluate for $eta_2=pi/4,pi/2,pi$ etc. (the upper limit for $eta_2$ should $le pi$ and not $<pi$), but I am not able to find the general expression from these particular cases.
$endgroup$
– Jog
Dec 15 '18 at 3:31