A new approach to the connection problem for local solutions to the general Heun equation

2016/06/28 by Fiziev, P. P.
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1606.08539

Abstract

We present new solution of the the connection problem for local solutions to the general Heun equation. Our approach is based on the symmetric form of the Heun's differential equation \citeFiziev14,Fiziev16 with four different regular singular points z_1,2,3,4. The four special regular points in the complex plane: Z₁₂₃,Z₂₃₄,Z₃₄₁,Z₄₁₂ are the centers of the circles, defined by the different triplets \z_k,z_l,z_m\ with corresponding different indexes and play fundamental role, since the coefficients of the connection matrix can be expressed using the values of local solutions of the general Heun's equation at these points. A special case when all coefficients can be calculated using only one of the points Z_klm is also considered.

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