Neumann determinants of the massive Laplacian on constant curvature disks are expressed as convergent infinite series, with exact special-mass reductions for m^2 = -η/L^2 q(q+1).
Large Parameter Cases of the Gauss Hypergeometric Function
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We consider the asymptotic behaviour of the Gauss hypergeometric function when several of the parameters a, b, c are large. We indicate which cases are of interest for orthogonal polynomials (Jacobi, but also Krawtchouk, Meixner, etc.), which results are already available and which cases need more attention. We also consider a few examples of 3F2-functions of unit argument, to explain which difficulties arise in these cases, when standard integrals or differential equations are not available.
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Neumann scalar determinants on constant curvature disks
Neumann determinants of the massive Laplacian on constant curvature disks are expressed as convergent infinite series, with exact special-mass reductions for m^2 = -η/L^2 q(q+1).