(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find ∫ I_{n}(ζ) dθ , where ζ= cosθ and I_{n}(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 I_{n}(ζ) with respect to ζ.

2. Relevant equations

d/dζ I_{n}(ζ)=-P_{n-1}(ζ), where P_{n}(ζ) is the legendre function of the first kind.

I_{n}(ζ)= [P_{n-2}(ζ)-P_{n}(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.

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

Can you offer guidance or do you also need help?

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