For each value of J, we have rotational degeneracy, g j = (2J+1), so the rotational partition function is therefore ζ ζ rot = ∑ ∑ J = 0 ∞ ∞ g j e − − E J / k B T = ∑ ∑ J = 0 ∞ ∞ ( 2 J + 1 ) e − − J ( J + 1 ) B / k B T .