$$\ \int_0^{\pi} \bigl(\sin(x)\bigr)^{2n-2k+1} e^{a\cos(x)} dx , \qquad ,n,k\in\mathbb Z,a\in\mathbb R.$$ I tried to solve this integral by parts, but I didn't get any result. I look forward to your experience.

$$\ \int_0^{\pi} \bigl(\sin(x)\bigr)^{2n-2k+1} e^{a\cos(x)} dx , \qquad a,n,k\in\mathbb Z.$$ I tried to solve this integral by parts, but I didn't get any result. I look forward to your experience.

$$\ \int_0^{\pi} \bigl(\sin(x)\bigr)^{2n-2k+1} e^{a\cos(x)} dx , \qquad a,n,k\in\mathbb Z.$$ I tried to solve this integral by parts, but I didn't get any result. I look forward to your experience.

$$\ \int_0^{\pi} \bigl(\sin(x)\bigr)^{2n-2k+1} e^{a\cos(x)} dx , \qquad ,n,k\in\mathbb Z,a\in\mathbb R.$$ I tried to solve this integral by parts, but I didn't get any result. I look forward to your experience.

$$\ \int_0^{\pi} \big(\sin(x)\big)^{2n-2k+1} e^{a\cos(x)} dx , \qquad a,n,k\in\mathbb Z$$ I tried to solve this integral by part , but I didn't get any result. I look forward to your experience

$$\ \int_0^{\pi} \bigl(\sin(x)\bigr)^{2n-2k+1} e^{a\cos(x)} dx , \qquad a,n,k\in\mathbb Z.$$ I tried to solve this integral by parts, but I didn't get any result. I look forward to your experience.