ABSTRACT
Mahajan’s Inequality If Jν is the Bessel function of the first kind then
(x+ 1)ν+1Jν
( π
x+ 1
) − xν+1Jν
(π x
) > (π 2
)ν 1 ν! .
References Lorch & Muldoon [180], Mahajan [190].
Mahler’s Inequalities If K ⊂ Rn is convex and compact, with ◦K 6= ∅ and centroid the origin, then
|K| |K∗| ≥ (n+ 1) n+1
(n!)2 ,
with equality if and only if K is the simplex with centroid the origin. If K is symmetric with respect to the origin, then
|K| |K∗| ≥ 4 n
n! ,
with equality if and only if K is the n-cube [−1, 1]n.
