A Mehler-Dirichlet integral is given by
![P_n(cosalpha)=(sqrt(2))/piint_0^alpha(cos[(n+1/2)phi])/(sqrt(cosphi-cosalpha))dphi,](/images/equations/Mehler-DirichletIntegral/NumberedEquation1.svg) |
where 
is a Legendre polynomial.
Mehler-Dirichlet Integral
See also
Laplace-Mehler Integral, Laplace's Integral, Legendre PolynomialExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Mehler-Dirichlet Integral." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Mehler-DirichletIntegral.html