Product formulas for the relativistic and nonrelativistic conical functions
Paper in proceedings, 2018

The conical function and its relativistic generalization can be viewed as eigenfunctions of the reduced 2-particle Hamiltonians of the hyperbolic Calogero-Moser system and its relativistic generalization. We prove new product formulas for these functions. As a consequence, we arrive at explicit diagonalizations of integral operators that commute with the 2-particle Hamiltonians and reduced versions thereof. The kernels of the integral operators are expressed as integrals over products of the eigenfunctions and explicit weight functions. The nonrelativistic limits are controlled by invoking novel uniform limit estimates for the hyperbolic gamma function.

product formulas

quantum Calogero-Moser systems

conical function


Martin Hallnäs

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Simon Ruijsenaars

University of Leeds

Advanced Studies in Pure Mathematics

Vol. 76 195-245

Representation theory, special functions and Painlevé equations
Kyoto, Japan,

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