Integral representations, monotonic properties, and inequalities on extended central binomial coefficient

DOI10.1002/mma.8115zbMath1527.05011OpenAlexW4210485775MaRDI QIDQ6181821

Chun-Fu Wei

Publication date: 20 December 2023

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.8115

zbMATH Keywords

gamma functionintegral representationinequalitybinomial coefficientpolygamma functiondecreasing propertyduplication formulacentral binomial coefficientincreasing propertypower-exponential functionextended binomial coefficientextended central binomial coefficientKazarinoff's integral representationL'Hôpital type monotonicity rule

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Gamma, beta and polygamma functions (33B15) Combinatorial inequalities (05A20)

Related Items (2)

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 ⋮ Taylor's series expansions for real powers of two functions containing squares of inverse cosine function, closed-form formula for specific partial Bell polynomials, and series representations for real powers of pi

Cites Work

• Bounds for the ratio of two gamma functions
• Inequalities for binomial coefficients
• On complete monotonicity for several classes of functions related to ratios of gamma functions
• Lower bound of sectional curvature of Fisher-Rao manifold of beta distributions and complete monotonicity of functions involving polygamma functions
• Some properties of the Fuss-Catalan numbers
• Integral representations of the Catalan numbers and their applications
• Parametric improper integrals, Wallis formula and Catalan numbers
• Some limit formulas for the Gamma and Psi (or Digamma) functions at their singularities
• On Wallis' formula
• The inverse of a triangular matrix and several identities of the Catalan numbers
• Limit formulas for ratios between derivatives of the gamma and digamma functions at their singularities
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