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math.CA2021
Linear differential operators with polynomial coefficients generating generalised Sylvester-Kac matrices
Alexander Dyachenko, Mikhail Tyaglov
A method of generating differential operators is used to solve the spectral problem for a generalisation of the Sylvester-Kac matrix. As a by-product, we find a linear differential…
math.CV2021★ 1 cited
Ratios of the Gauss hypergeometric functions with parameters shifted by integers: part I
Alexander Dyachenko, Dmitrii Karp
We consider the ratio of two Gauss hypergeometric functions with real parameters shifted by arbitrary integers. We find a formula for the jump of this ratio over the branch cut in…