Formulas for factorial $N$

Finite N Fluctuation Formulas for Random Matrices

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic N j=1 x j − x is computed exactly and shown to satisfy a central limit theorem as N → ∞. For the circular random matrix ensemble the p.d.f.'s for the linear statistics 1 2 N j=1 (θ j −π) and − N j=1 log 2| sin θ j /2| are calculated exactly by using a constant term identity ...

Voronoi formulas on GL ( n )

In this paper, we give a new, simple, purely analytic proof of the Voronoi formula for Maass forms on GL(3) first derived by Miller and Schmid. Our method is based on two lemmas of the first author and Thillainatesan which appear in their recent non-adelic proof of the converse theorem on GL(3). Using a different, even simpler method we derive Voronoi formulas on GL(n) twisted by additive chara...

Efficacy of commercial formulas in comparison with home-made formulas for enteral feeding: A critical review

Background: In several disease conditions, patients must inevitably be nourished by enteral feeding (EF). Though in many countries, commercial formulas are routinely used for EF, in Iran still home-made formulas are commonly employed as commercial formulas are not covered by insurance. This may pose patients to malnutrition and bring about further costs.  The aim of this study was to evalu...

Product Formulas for Modular Forms on O(2, N)

On Dimension Formulas for gl(m|n) Representations

We investigate new formulas for the dimension and superdimension of covariant representations Vλ of the Lie superalgebra gl(m|n). The notion of t -dimension is introduced, where the parameter t keeps track of the Z-grading of Vλ . Thus when t = 1, the t -dimension reduces to the ordinary dimension, and when t = −1 it reduces to the superdimension. An interesting formula for the t -dimension is ...