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Integrating the Gegenbauer function (1st kind) wrt theta

  1. Aug 20, 2011 #1
    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
  2. jcsd
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