# Closed form solutions to integrals of the following type?

1. Feb 24, 2013

### eyesontheball1

For any integral where the integrand is of the form f(θ)^z, with z a complex number, and f(θ) = sin(θ), cos(θ), tan(θ), .... etc., θ being either real or complex. Is it possible to explicitly solve for an antiderivative? I'm not aware of any such way I could use residues/series representations here, and I've tried all kinds of substitutions for integrals of this type; in particular, of [sin(θ)]^z, z being a complex constant. Thank you in advance!!!!!

Best,
David

2. Feb 24, 2013

### mathman

No, even if z is real (not rational).

3. Feb 24, 2013

### JJacquelin

Hi!

most of them can be expressed in terms of hypergeometric functions.

4. Feb 25, 2013

### eyesontheball1

Would you mind showing exactly how such an integral can be expressed via a hypergeometric function? Thanks in advance!

5. Feb 25, 2013

### JJacquelin

6. Feb 27, 2013

### eyesontheball1

Great, thank you JJacquelin!