
Normal Ordering in the Weyl Algebra – Further Aspects 193
6.1.4 The Identity of Bender, Mead, and Pinsky
In this section, we describe an identity first observed by Bender, Mead, and Pinsky
[82, 83] and discussed in the context of operator ordering by Bender and Dunne [81]. It
was first proved by Koornwinder [680], who used several intricate relations. Later, it was
reproved and discussed by other authors [527,1004]. We follow the presentation given in [527]
and consider the Weyl algebra A
i
generated by U and V satisfying UV − VU = i.Letus
denote by T
n,m
the sum of all possible terms containing n factors of U and m factors of
V .Also,T
n
= T
n,n
. For example, ...