Белратюк, Леонід ПетровичБедратюк, Ганна ІванівнаBedratyuk, L.Bedratyuk, A.2019-12-102019-12-102018Bedratyuk L. The inverse and derivative connecting problems for some hypergeometric polynomials / L. Bedratyuk, A. Bedratyuk // Carpathian Mathematical Publications. – 2018. – Vol. 10, № 2. – P. 235–247. doi:10.15330/cmp.10.2.235-2472075-9827(Print), 2313-0210(Online)https://elar.khmnu.edu.ua/handle/123456789/8045Given two polynomial sets { P n ( x )} n ≥ 0 and { Q n ( x )} n ≥ 0 such that deg ( P n ( x )) = deg ( Q n ( x )) = n. The so-called connection problem between them asks to find coefficients α n,k in the expression Q n ( x ) = n ∑ k = 0 α n,k P k ( x ) . The connectionproblem for different typesof polynomials has along history, and it is still of interest. The connection coefficients play an important role in many problems in pure and applied mathematics, especially in combinatorics, mathematical physics and quantum chemical applications. For the particular case Q n ( x ) = x n the connection problem is called the inversion problem associated to { P n ( x )} n ≥ 0 . The particular case Q n ( x ) = P ′ n + 1 ( x ) is called the derivative connecting problem for polynomial family { P n ( x )} n ≥ 0 . In this paper, we give a closed- form expression of the inversion and the derivative coefficients for hypergeometric polynomials of the formenconnection probleminversion problemderivative connecting problemhypergeometric functionsСтаття