Results 11 to 20 of about 57,853 (286)
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
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On the summation formula of Voronoi [PDF]
Transactions of the American Mathematical Society, 1972 A formula involving sums of the form _ d(n)f(n) and _ d(n)g(n) is derived, where d(n) is the number of divisors of n, andf(x), g(x) are Hankel transforms of each other. Many forms of such a formula, generally known as Voronoi's summation formula, are known, but we give a more symmetrical formula.
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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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Analogues of Euler and Poisson summation formulae [PDF]
, 2002 Euler--Maclaurin and Poisson analogues of the summations $\sum_{a < n \leq b} \chi(n) f(n)$, $\sum_{a < n \leq b} d(n) f(n)$, $\sum_{a < n \leq b} d(n) \chi (n) f(n)$ have been obtained in a unified manner, where $(\chi (n))$ is a periodic complex ...
Rane, Vivek V
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Construction of partially degenerate Laguerre–Bernoulli polynomials of the first kind
Applied Mathematics in Science and Engineering, 2022 In this paper, we introduce partially degenerate Laguerre–Bernoulli polynomials of the first kind and deduce some relevant properties by using a preliminary study of these polynomials.
Waseem A. Khan +2 more
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Infinite Series Concerning Tails of Riemann Zeta Values
Axioms, 2023 Infinite series involving Riemann’s zeta and Dirichlet’s lambda tails, and weighted by three harmonic-like elementary symmetric functions are examined.
Chunli Li, Wenchang Chu
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On a new class of summation formulae involving the Laguerre polynomial [PDF]
, 2012 By elementary manipulation of series, a general transformation involving the generalized hypergeometric function is established. Kummer’s first theorem, the classical Gauss summation theorem and the generalized Kummer summation theorem due to Lavoie et ...
Kim, Yong S. +2 more
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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.
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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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