Results 21 to 30 of about 56,637 (162)
Explicit Construction of the Inverse of an Analytic Real Function: Some Applications
Mathematics, 2020 In this paper, we introduce a general procedure to construct the Taylor series development of the inverse of an analytical function; in other words, given y=f(x), we provide the power series that defines its inverse x=hf(y). We apply the obtained results
Joaquín Moreno +2 more
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Coinciding Mean of the Two Symmetries on the Set of Mean Functions
Axioms, 2023 On the set M of mean functions, the symmetric mean of M with respect to mean M0 can be defined in several ways. The first one is related to the group structure on M, and the second one is defined trough Gauss’ functional equation.
Lenka Mihoković
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Integral Representations of the Catalan Numbers and Their Applications
Mathematics, 2017 In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations ...
Feng Qi, Bai-Ni Guo
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On a congruence involving $q$-Catalan numbers
Comptes Rendus. Mathématique, 2020 Based on a $q$-congruence of the author and Petrov, we set up a $q$-analogue of Sun–Tauraso’s congruence for sums of Catalan numbers, which extends a $q$-congruence due to Tauraso.
Liu, Ji-Cai
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On a Surface Associated to the Catalan Triangle
Axioms, 2022 We define a surface that interpolates the ballot numbers in the Catalan triangle corresponding to every pair of nonnegative integers (except for the origin).
Marilena Jianu +5 more
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Determinants of (generalised) Catalan numbers [PDF]
, 2010 We show that recent determinant evaluations involving Catalan numbers and generalisations thereof have most convenient explanations by combining the Lindstr\"om-Gessel-Viennot theorem on non-intersecting lattice paths with a simple determinant lemma from
Krattenthaler, Christian
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Some Families of Apéry-Like Fibonacci and Lucas Series
Mathematics, 2021 In this paper, the authors investigate two special families of series involving the reciprocal central binomial coefficients and Lucas numbers. Connections with several familiar sums representing the integer-valued Riemann zeta function are also pointed ...
Robert Frontczak +2 more
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A note on log-convexity of q-Catalan numbers [PDF]
, 2007 The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q=1, to the Catalan numbers: 1, 1, 2, 5, 14,..., a log-convex sequence.
Butler, L. M., Flanigan, W. P.
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Alternating Convolutions of Catalan Numbers [PDF]
Bulletin of the Brazilian Mathematical Society, New Series, 2021 A new class of alternating convolutions concerning binomial coefficients and Catalan numbers are evaluated in closed forms.
openaire +3 more sources
Convolution identities involving the central binomial coefficients and Catalan numbers [PDF]
Transactions on Combinatorics, 2021 We generalize some convolution identities due to Witula and Qi et al. involving the central binomial coefficients and Catalan numbers. Our formula allows us to establish many new identities involving these important quantities, and recovers some ...
Necdet Batır, Hakan Kucuk, Sezer Sorgun
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