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Strong asymptotics for Jacobi-Piñeiro orthogonal polynomials
Sergei Kalmykov, Vladimir Lysov, Vinay Shukla
We investigate the asymptotic behavior of Jacobi-Piñeiro polynomials of degree orthogonal on with respect to weights , where $α_1,α_2,…
Evaluation of terminating and non-terminating sums containing the digamma function
Sergei Kalmykov, Dmitrii Karp, Vinay Shukla
We derive transformation and summation formulas for terminating and nonterminating series involving the digamma function. Our principal results are obtained by a limiting process s…
On Askey's extension of Clausen's identity and its polynomial perturbation
Dmitrii Karp, Vinay Shukla
The celebrated Clausen's identity expresses the square of the Gauss hypergeometric series as a single hypergeometric series. Goursat showed in…
Stability of the Toda equations related to a perturbed type recurrence relation
Vinay Shukla, A. Swaminathan
In this manuscript, a modified type recurrence relation is considered whose recurrence coefficients are perturbed by addition or multiplication of a constant. The perturbed s…
Generalized co-polynomials of type and associated quadrature rules
Vinay Shukla, A. Swaminathan
When the co-recursion and co-dilation in the recurrence relation of certain sequences of orthogonal polynomials are not at the same level, the behaviour of the modified orthogonal…
Spectral properties related to generalized complementary Romanovski-Routh polynomials
Vinay Shukla, A. Swaminathan
Complementary Romanovski-Routh polynomials play an important role in extracting specific properties of orthogonal polynomials. In this work, a generalized form of the Complementary…
Chain sequences and Zeros of a perturbed type recurrence relation
Vinay Shukla, A. Swaminathan
In this manuscript, new algebraic and analytic aspects of the orthogonal polynomials satisfying type recurrence relation given by \begin{align*} \mathcal{P}_{n+1}(x) = (x-…
Spectral transformation associated with a perturbed type recurrence relation
Vinay Shukla, A. Swaminathan
In this work, orthogonal polynomials satisfying type recurrence relation % with $\mathcal{P}_…