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Approximating real Pochhammer products: a comparison with powers

Vito Lampret (2009)

Open Mathematics

Accurate estimates of real Pochhammer products, lower (falling) and upper (rising), are presented. Double inequalities comparing the Pochhammer products with powers are given. Several examples showing how to use the established approximations are stated.

Approximation of the Stieltjes integral and applications in numerical integration

Pietro Cerone, Sever Silvestru Dragomir (2006)

Applications of Mathematics

Some inequalities for the Stieltjes integral and applications in numerical integration are given. The Stieltjes integral is approximated by the product of the divided difference of the integrator and the Lebesgue integral of the integrand. Bounds on the approximation error are provided. Applications to the Fourier Sine and Cosine transforms on finite intervals are mentioned as well.

Asymmetric covariance estimates of Brascamp–Lieb type and related inequalities for log-concave measures

Eric A. Carlen, Dario Cordero-Erausquin, Elliott H. Lieb (2013)

Annales de l'I.H.P. Probabilités et statistiques

An inequality of Brascamp and Lieb provides a bound on the covariance of two functions with respect to log-concave measures. The bound estimates the covariance by the product of the L 2 norms of the gradients of the functions, where the magnitude of the gradient is computed using an inner product given by the inverse Hessian matrix of the potential of the log-concave measure. Menz and Otto [Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential....

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