# Integrating the Gegenbauer function (1st kind) wrt theta

1. Aug 20, 2011

### Ariana1983

1. The problem statement, all variables and given/known data

Find ∫ In(ζ) dθ , where ζ= cosθ and In(ζ) is the gegenbauer function of the first kind.

The original problem is to find find ∫ sinθ *I//n(ζ) dθ where I//n= 2nd differential of In(ζ) with respect to ζ.

2. Relevant equations

d/dζ In(ζ)=-Pn-1(ζ), where Pn(ζ) is the legendre function of the first kind.

In(ζ)= [Pn-2(ζ)-Pn(ζ)]/(2n-1)

3. The attempt at a solution

I know d/dθ= d/dζ * dζ/dθ = -sinθ*d/dζ by the chain rule since ζ=cosθ, but how to apply that to integration of the gegenbauer with respect to theta? I came across that problem as I used integration via parts to solve the original problem.

Last edited: Aug 20, 2011