12 citations · 37 across the 19 of their papers we have counts for
10 papers · 1 filter
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…
A new identity for the sum of products of generalized basic hypergeometric functions
S. I. Kalmykov, D. Karp, A. Kuznetsov
We prove a duality relation for generalized basic hypergeometric functions. It forms a -extension of a recent result of the second and the third named authors and generalizes bo…
Inequalities for some basic hypergeometric functions
S. I. Kalmykov, D. B. Karp
We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shi…
New identities for a sum of products of the Kummer functions
S. I. Kalmykov, D. B. Karp
Recently, Feng, Kuznetsov and Yang discovered a very general reduction formula for a sum of products of the generalized hypergeometric functions (J. Math. Anal. Appl. 443(2016), 11…
Higher Markov and Bernstein inequalities and fast decreasing polynomials with prescribed zeros
Sergei Kalmykov, Béla Nagy
Higher order Bernstein- and Markov-type inequalities are established for trigonometric polynomials on compact subsets of the real line and algebraic polynomials on compact subsets…
Log-concavity and Turán-type inequalities for the generalized hypergeometric function
S. I. Kalmykov, D. B. Karp
The paper studies logarithmic convexity and concavity of the generalized hypergeometric function with respect to simultaneous shift of several parameters. We use integral represent…
Bernstein type inequalities for rational functions on analytic curves and arcs
Sergei Kalmykov, Béla Nagy
Borwein and Erdélyi proved a Bernstein type inequality for rational functions on the unit circle and on the real line. Here we establish asymptotically sharp extensions of their in…
Log-convexity and log-concavity for series in gamma ratios and applications
S. I. Kalmykov, D. B. Karp
Polynomial sequence is -logarithmically concave if is a polynomial with nonnegative coefficients for any . We introduce an an…
Log-concavity for series in reciprocal gamma functions and applications
S. I. Kalmykov, D. B. Karp
Euler's gamma function is logarithmically convex on positive semi-axis. Additivity of logarithmic convexity implies that the function sum of gammas with non-negative coefficients i…