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spaces separating dx and dy
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edit approved May 7 at 16:21
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edit approved May 7 at 16:21
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Integration of $\int\limits_0^{2\pi} \int\limits_0^{2\pi} {\min\min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)}} \, dx \, dy$

$$\int\limits_0^{2\pi} \int\limits_0^{2\pi} {\min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)}} dx dy, \qquad a\in\mathbb R. $$$$\int\limits_0^{2\pi} \int\limits_0^{2\pi} \min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)} \, dx \, dy, \qquad a\in\mathbb R. $$ I tried to find the value of the integral following the method proposed in this example: however I didn't succeed so I posted the question here looking forward to your experience.

Integration of $\int\limits_0^{2\pi} \int\limits_0^{2\pi} {\min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)}} dx dy$

$$\int\limits_0^{2\pi} \int\limits_0^{2\pi} {\min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)}} dx dy, \qquad a\in\mathbb R. $$ I tried to find the value of the integral following the method proposed in this example: however I didn't succeed so I posted the question here looking forward to your experience.

Integration of $\int\limits_0^{2\pi} \int\limits_0^{2\pi} \min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)} \, dx \, dy$

$$\int\limits_0^{2\pi} \int\limits_0^{2\pi} \min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)} \, dx \, dy, \qquad a\in\mathbb R. $$ I tried to find the value of the integral following the method proposed in this example: however I didn't succeed so I posted the question here looking forward to your experience.

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Daniele Tampieri
Daniele Tampieri
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Integration of $$\int\limits_0^$\int\limits_0^{2\pi} \int\limits_0^{2\pi} {\min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)}} dx dy$$dy$

Minor Math Jaxing and grammar improvements
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Daniele Tampieri
Daniele Tampieri
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Integration of $\int_0^$$\int\limits_0^{2\pi} \int_0^\int\limits_0^{2\pi} \min{\min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)}} dx dy$dy$$

$$\int_0^{2\pi} \int_0^{2\pi} \min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)} dx dy, \qquad a\in\mathbb R$$$$\int\limits_0^{2\pi} \int\limits_0^{2\pi} {\min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)}} dx dy, \qquad a\in\mathbb R. $$ I tried to find the integral like thisvalue of the integral following the method proposed in (https://math.stackexchange.com/q/2346355this example) but: however I couldn't,didn't succeed so I lookposted the question here looking forward to your experience.

Integration of $\int_0^{2\pi} \int_0^{2\pi} \min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)} dx dy$

$$\int_0^{2\pi} \int_0^{2\pi} \min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)} dx dy, \qquad a\in\mathbb R$$ I tried to find the integral like this integral (https://math.stackexchange.com/q/2346355) but I couldn't, I look forward to your experience.

Integration of $$\int\limits_0^{2\pi} \int\limits_0^{2\pi} {\min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)}} dx dy$$

$$\int\limits_0^{2\pi} \int\limits_0^{2\pi} {\min \{ x-y, 2\pi- (x-y) \} e^{a\cos(x)} e^{a\cos(y)}} dx dy, \qquad a\in\mathbb R. $$ I tried to find the value of the integral following the method proposed in this example: however I didn't succeed so I posted the question here looking forward to your experience.

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AK Math
AK Math
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