New solutions for the elliptic Darboux equation are obtained as particular cases of constructed Heun's general equation. We consider two groups power series expansions and new in Gauss hypergeometric functions. The convergence one group is determined by means ratio tests infinite series, while other designed to solve problems which admit finite-series solutions. Actually, we envisage periodic q...

We present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to analysis wave equation on AdS-Schwarzschild background. is computed from connection coefficients Heun equation, which can be expressed terms Nekrasov-Shatashvili partition SU(2) supersymmetric gauge theory with four fundamental hype...

We calculate analytically the asymptotic form of quasi-normal frequencies for massive scalar perturbations of large black holes in AdS5. We solve the wave equation, which reduces to a Heun equation, perturbatively and calculate the wave function as an expansion in 1/m, where m is the mass of the mode. The zeroth-order results agree with expressions derived by numerical analysis. We also calcula...

The edge detour index polynomials were recently introduced for computing the edge detour indices. In this paper we find relations among edge detour polynomials for the 2-dimensional graph of $TUC_4C_8(S)$ in a Euclidean plane and $TUC4C8(S)$ nanotorus.

In this work we solve the angular Teukolsky equation in alternative way for a more general case τ ≠ 0 but m = , s . We first transform to confluent Heun differential and then construct Wronskian determinant calculate eigenvalues normalized eigenfunctions. find that larger l are approximately given by A ≈ [ ( + 1 ) - R 2 / ] i I with an arbitrary The probability distribution (APD) ground state m...

Two sets of the Heun functions are introduced via integrals. Theorems about expanding functions with respect to these sets are proven. A number of integral and series representations as well as integral equations and asymptotic formulas are obtained for these functions. Some of the coefficients of the series are orthogonal (J-orthogonal) functions of discrete variables and may be interpreted as...