Hi,

> f = (2*l+1) / (2*t) * Integral(legendre(l, (1-R**2+t**2) / (2*t)) *
> exp(-alpha*R), (R, 1-t, 1+t))

BTW: probably this integral does not have a closed form,
not even in terms of pFq or even higher functions:

http://www.wolframalpha.com/input/?i=Integral%28exp%28-R*alpha%29*LegendreP[l%2C+%28-R**2+%2B+t**2+%2B+1%29%2F%282*t%29]%2C+R%29
http://www.wolframalpha.com/input/?i=Integral%28exp%28-R*alpha%29*LegendreP[l%2C+%28-R**2+%2B+t**2+%2B+1%29%2F%282*t%29]%2C+R%2C+1-t%2C+1%2Bt%29

http://integrals.wolfram.com/index.jsp?expr=Exp[-x*a]*LegendreP[l%2C+%28-x**2+%2B+t**2+%2B+1%29%2F%282*t%29]&random=false

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