A specific integral

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Consider the following integral
$$int_0^pi e^acostheta sin^ntheta mathrmdtheta, $$
where $a$ is a real number and $n$ is an integer.



Is it possible to relate the integral given above to any special function?



My guess is that it should be some kind of Bessel function.
But I am not able to solve it.




integration special-functions




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  • In general it is connected with a "regularised confluent hypergeometric function". See Wolfram.
    – uniquesolution
    6 hours ago














up vote
-2
down vote

favorite












Consider the following integral
$$int_0^pi e^acostheta sin^ntheta mathrmdtheta, $$
where $a$ is a real number and $n$ is an integer.



Is it possible to relate the integral given above to any special function?



My guess is that it should be some kind of Bessel function.
But I am not able to solve it.




integration special-functions




share|cite|improve this question





















  • In general it is connected with a "regularised confluent hypergeometric function". See Wolfram.
    – uniquesolution
    6 hours ago












up vote
-2
down vote

favorite









up vote
-2
down vote

favorite











Consider the following integral
$$int_0^pi e^acostheta sin^ntheta mathrmdtheta, $$
where $a$ is a real number and $n$ is an integer.



Is it possible to relate the integral given above to any special function?



My guess is that it should be some kind of Bessel function.
But I am not able to solve it.




integration special-functions




share|cite|improve this question













Consider the following integral
$$int_0^pi e^acostheta sin^ntheta mathrmdtheta, $$
where $a$ is a real number and $n$ is an integer.



Is it possible to relate the integral given above to any special function?



My guess is that it should be some kind of Bessel function.
But I am not able to solve it.





integration special-functions





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 7 hours ago









amWhy

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  • In general it is connected with a "regularised confluent hypergeometric function". See Wolfram.
    – uniquesolution
    6 hours ago
















  • In general it is connected with a "regularised confluent hypergeometric function". See Wolfram.
    – uniquesolution
    6 hours ago















In general it is connected with a "regularised confluent hypergeometric function". See Wolfram.
– uniquesolution
6 hours ago




In general it is connected with a "regularised confluent hypergeometric function". See Wolfram.
– uniquesolution
6 hours ago















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