The inverse and derivative connecting problems for some hypergeometric polynomials
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Дата
2018
Автори
Белратюк, Леонід Петрович
Бедратюк, Ганна Іванівна
Bedratyuk, L.
Bedratyuk, A.
Назва журналу
Номер ISSN
Назва тому
Видавець
Прикарпатський національний університет імені Василя Стефаника
Анотація
Given 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 form
Опис
Ключові слова
connection problem, inversion problem, derivative connecting problem, hypergeometric functions
Бібліографічний опис
Bedratyuk 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.10.2.235-247