Errata for Taylor-Woodward

As pointed out to us by Francesco Costantino:

(1) There are sequences of 6j symbols obtained by re-scaling with infinitely many zeroes, so that the definition of convergence does not make sense.

In this case, the definition of asymptotic convergence may be replaced with the following: We say that two functions f,g of a positive integer k are asympotically convergent if and only if f(k) - g(k) is o(1/k)f(k), or equivalently, f(k) - g(k) is o(1/k) g(k).

The main result of the paper shows something stronger, namely if f and g denote the 6j symbols and asymptotic formula respectively, then f(k) - g(k) is o(k^{-2}), whereas f(k) goes like k^{-3/2}. Thus, the statement and proof in this caes are the same.

(2) A sign is missing in Schlafli's formula (or alternatively, the dihedral angles should be interior.)

(3) As pointed out to us by Bruce Bartlett and V. Hosana Ranaivomanana, the statement of Proposition 2.4.1.(n) in contains a typo. The left hand side should not be inverted.

Back to my homepage .