We study spherical quadrilaterals whose angles are odd multiples of π/2, and the equivalent accessory parameter problem for the Heun equation. We obtain a classification of these quadrilaterals up to isometry. For given angles, there are finitely many one-dimensional continuous families which we enumerate. In each family the conformal modulus is either bounded from above or bounded from below, ...

We investigate the relation between the four dimensional N = 2 SU(2) super Yang-Mills theory with four fundamental flavors and the quantum mechanics model with Treibich-Verdier potential described by the Heun equation in the elliptic form. We study the precise correspondence of quantities in the gauge theory and the quantum mechanics model. An iterative method is used to obtain the asymptotic e...

Upon solving a finite discrete reduction in the difference Heun equation, we arrive at an elliptic generalization of Racah polynomials. We exhibit three-term recurrence relation and orthogonality relations for these The well-known q-Racah polynomials Askey Wilson are recovered as trigonometric limit.

We are considering the spacetime described by metric proposed Mannheim and Kazanas. The effective potential circular orbits discussed. rotational velocity derived from geodesics equation agrees with observed flat galactic rotation curves. Finally, solutions to Gordon for massless bosons evolving in this obtained terms of Heun general functions.

A recently proposed algorithm to obtain global solutions of the double confluent Heun equation is applied to solve the quantum mechanical problem of finding the energies and wave functions of a particle bound in a potential sum of a repulsive supersingular term, A r, plus an attractive Coulombian one, −Z r. The existence of exact algebraic solutions for certain values of A is discussed. Supersi...

Classical Virasoro conformal blocks are believed to be directly related accessory parameters of Floquet type in the Heun equation and some its confluent versions. We extend this relation another class parameter functions that defined by inverting all-order Bohr–Sommerfeld periods for biconfluent equation. The relevant involve Nagoya irregular vertex operators rank 1 2 conjecturally correspond p...