10 citations · 35 across the 15 of their papers we have counts for
16 papers
Trigonometric identities: from Hermite via Meijer, Nørlund and Braaksma to Chu and Johnson and beyond
Alexander Dyachenko, Dmitrii Karp
Known already to the ancient Greeks, today trigonometric identities come in a large variety of tastes and flavours. In this large family there is a subfamily of interpolation-like…
On the spectrum of the tridiagonal matrices with two-periodic main diagonal
Alexander Dyachenko, Mikhail Tyaglov
We find the spectrum and eigenvectors of an arbitrary irreducible complex tridiagonal matrix with two-periodic main diagonal provided that the spectrum and eigenvectors of the matr…
Ratios of the Gauss hypergeometric functions with parameters shifted by integers: more on integral representations
Alexander Dyachenko, Dmitrii Karp
We consider the ratio of two Gauss hypergeometric functions, in which the parameters of the numerator function differ from the respective parameters of the denominator function by…
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…
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…
Coefficientwise total positivity of some matrices defined by linear recurrences
Xi Chen, Bishal Deb, Alexander Dyachenko +2
We exhibit a lower-triangular matrix of polynomials in six indeterminates that appears empirically to be coefficientwise totally positive, and which includes as a…