An Integral of Ramanujan and Orthogonal Polynomials

Introduction, beta integrals and Jacobi polynomials. A classical beta integral has the form
∫[l₁(t)]^a[l₂(t)]^bdt (1.1)
where l₁(t) and l₂(t) are linear functions, a and b are complex numbers, and C is an appropriate contour. Two important cases are Euler’s integral.