On Gamma function inequalities
Mathematics of Computation
Inequalities and monotonicity properties for gamma and q-gamma functions
Proceedings of the conference on Approximation and computation : a fetschrift in honor of Walter Gautschi: a fetschrift in honor of Walter Gautschi
On some inequalities for the gamma and psi functions
Mathematics of Computation
Unified treatment of Gautschi-Kershaw type inequalities for the gamma function
Journal of Computational and Applied Mathematics
Inequalities and monotonicity properties for the gamma function
Journal of Computational and Applied Mathematics - Special issue on orthogonal polynomials, special functions and their applications
On the maximum value of Jacobi polynomials
Journal of Approximation Theory
On the maximum value of Jacobi polynomials
Journal of Approximation Theory
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We present a survey of the most recent results and inequalities for the gamma function and the ratio of the gamma functions and study, among other things, the relation between these results and known inequalities for ultraspherical polynomials. In particular, we discuss the inequality (sin θ)λ|Pn(λ)(cos θ)| 1-λ/Γ(λ) Γ(n + 3/2λ)/Γ(n + 1 + 1/2λ), 0 ≤ θ ≤ π, where Pn(λ)(cos θ) denotes the ultraspherical polynomial of degree n, established by Alzer (Arch. Math. 69 (1997) 487) and the one established by Durand (In: R.A. Askey (Ed.), Theory and Application of Special Functions, Proceedings of the Advanced Seminar on Mathematical Research Center, University of Wisconsin, Madison, Vol. 35, Academic Press, New York, 1975, p. 353) (sin θ)λ|Pn(λ)(cos θ)| ≤ Γ(n/2 + λ)/Γ(λ)Γ(n/2 + 1), 0 ≤ θ ≤ π.