Integral representations of the Catalan numbers and their applications
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Publication:2413128
DOI10.3390/math5030040zbMath1402.11032OpenAlexW2610704385MaRDI QIDQ2413128
Publication date: 9 April 2018
Published in: Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3390/math5030040
beta functionCatalan numberintegral representationapplicationCatalan-Qi functionCatalan-Qi numbersum of power seriesequivalent relation
Related Items
Catalan-Qi numbers, series involving the Catalan-Qi numbers and a Hankel determinant evaluation ⋮ The inverse versine function and sums containing reciprocal central binomial coefficients and reciprocal Catalan numbers ⋮ Several explicit and recursive formulas for generalized Motzkin numbers ⋮ MacLaurin’s series expansions for positive integer powers of inverse (hyperbolic) sine and tangent functions, closed-form formula of specific partial Bell polynomials, and series representation of generalized logsine function ⋮ The inverse of a triangular matrix and several identities of the Catalan numbers ⋮ Integral representations of the Catalan numbers and their applications ⋮ Explicit formulas and recurrence relations for generalized Catalan numbers ⋮ Catalan generating functions for bounded operators ⋮ Integral representations, monotonic properties, and inequalities on extended central binomial coefficient ⋮ Several identities and relations related to \(q\)-analogues of Pochhammer \(k\)-symbol with applications to Fuss-Catalan-Qi numbers ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Enumerative combinatorics of \textit{XX0} Heisenberg chain ⋮ Unnamed Item ⋮ A ratio of finitely many gamma functions and its properties with applications ⋮ Integral representations of the large and little Schröder numbers ⋮ Catalan and Motzkin integral representations ⋮ Several formulas and identities related to Catalan-Qi and \(q\)-Catalan-Qi numbers ⋮ Catalan-like number sequences and Hausdorff moment sequences ⋮ On complete monotonicity for several classes of functions related to ratios of gamma functions ⋮ Several series identities involving the Catalan numbers ⋮ A note on Vietoris' number sequence ⋮ On the Catalan numbers and some of their identities ⋮ A note on the sequence related to Catalan numbers ⋮ Some properties of the Fuss-Catalan numbers ⋮ Catalan generating functions for generators of Uni-parametric families of operators ⋮ An integral representation, complete monotonicity, and inequalities of the Catalan numbers
Uses Software
Cites Work
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