Results 11 to 20 of about 117,044 (300)
Some Formulae of Products of the Apostol-Bernoulli and Apostol-Euler Polynomials [PDF]
Discrete Dynamics in Nature and Society, 2012 Some formulae of products of the Apostol-Bernoulli and Apostol-Euler polynomials are established by applying the generating function methods and some summation transform techniques, and various known results are derived as special cases.
Yuan He, Chunping Wang
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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
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Further Closed Formulae of Exotic 3F2-Series
Axioms, 2023 By making use of the linearization method, we examine a class of nonterminating 3F2-series with five free integer parameters that yields twenty summation formulae.
Wenchang Chu
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Implicit Summation Formula for 2-Variable Laguerre-Based Poly-Genocchi Polynomials [PDF]
International Journal of Analysis and Applications, 2018 The main object of this paper is to introduce a new class of Laguerre-based poly-Genocchi polynomials and investigate some properties for these polynomials and related to the Stirling numbers of the second kind.
Waseem A. Khan +2 more
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Around the Lipschitz Summation Formula [PDF]
Mathematical Problems in Engineering, 2020 Boundary behavior of important functions has been an object of intensive research since the time of Riemann. Kurokawa, Kurokawa-Koyama, and Chapman studied the boundary behavior of generalized Eisenstein series which falls into this category. The underlying principle is the use of the Lipschitz summation formula.
Wenbin Li, Hongyu Li, Jay Mehta
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Summation formulas of q-hyperharmonic numbers [PDF]
Afrika Matematika, 2021 Afrika ...
Komatsu, Takao, Li, Rusen
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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
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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
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Summation formulae on reciprocal sequences
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.
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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
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