Results 11 to 20 of about 112,710 (299)
Summation formulae on reciprocal sequences [PDF]
European Journal of Combinatorics, 2007 Given a sequence \(\{a_n\}_{n\geq0}\) of complex numbers, the reviewer [Eur. J. Comb. 24, 709--718 (2003; Zbl 1024.05010)] introduced its dual sequence \(\{a_n^*\}_{n\geq0}\) with \(a_n^*=\sum_{k=0}^n\binom {n}{k}(-1)^ka_k\), and set \[ A_n(x)=\sum_{k=0}^n\binom{n}{k}(-1)^ka_kx^{n-k}\quad \text{and}\quad A_n^*(x)=\sum_{k=0}^n\binom{n}{k}(-1)^ka_k^*x^{n-
CHU, Wenchang, MAGLI P.
openaire +5 more sources
Summation formulae for basic hypergeometric functions via fractional q-calculus [PDF]
Le Matematiche, 2009 The object of this paper is to illustrate how the q-fractional calculus approach can be employed to derive a number of summation formulae for the generalized basic hypergeometric functions of one and more variables in terms of the q-gamma functions.
Sunil Dutt Purohit
doaj +2 more sources
Summation formulae for quadrics
Selecta MathematicaRemoved the appendix by C-H. Hsu at the request of the referee.
Getz, Jayce R.
core +5 more sources
Harmonic number identities via polynomials with r-Lah coefficients
Comptes Rendus. Mathématique, 2020 In this paper, polynomials whose coefficients involve $r$-Lah numbers are used to evaluate several summation formulae involving binomial coefficients, Stirling numbers, harmonic or hyperharmonic numbers.
Kargın, Levent, Can, Mümün
doaj +1 more source
A Family of Generalized Legendre-Based Apostol-Type Polynomials
Axioms, 2022 Numerous polynomials, their extensions, and variations have been thoroughly explored, owing to their potential applications in a wide variety of research fields.
Talha Usman +3 more
doaj +1 more source
Summation formulae involving the Laguerre polynomial [PDF]
, 1998 A general result involving the generalized hypergeometric function is deduced by the elementary manipulation of series. Kummer's first theorem for the confluent hypergeometric function and two summation formulae for the Gauss hypergeometric function are ...
Exton, H.
core +1 more source
A Note on Sequence of Functions associated with the Generalized Jacobi polynomial
Researches in Mathematics, 2023 An attempt is made to introduce and use operational techniques to study about a new sequence of functions containing generalized Jacobi polynomial. Some generating relations, finite summation formulae, explicit representation of a sequence of function ...
D. Waghela, S.B. Rao
doaj +1 more source
New Type of Degenerate Changhee–Genocchi Polynomials
Axioms, 2022 A remarkably large number of polynomials and their extensions have been presented and studied. In this paper, we consider a new type of degenerate Changhee–Genocchi numbers and polynomials which are different from those previously introduced by Kim.
Maryam Salem Alatawi, Waseem Ahmad Khan
doaj +1 more source
A Summation Formula for Macdonald Polynomials [PDF]
Letters in Mathematical Physics, 2016 We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases $t=1$ and $q=0$, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively.
de Gier, J, Wheeler, M
openaire +3 more sources
Holmgren problem for elliptic equation with singular coefficients
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2020 In the present work, we investigate the Holmgren problem for an multidimensional elliptic equation with several singular coefficients. We use a fundamental solution of the equation, containing Lauricella’s hypergeometric function in many variables.
Ergashev, T.G., Hasanov, A.
doaj +1 more source