def beta_expectation(a, b, k):
mysum = psi(a + b)
Elog_a = psi(a) - mysum
Elog_b = psi(b) - mysum
Elog_beta = n.zeros(k)
Elog_beta[0] = Elog_a[0]
# print Elog_beta
for i in range(1, k):
Elog_beta[i] = Elog_a[i] + n.sum(Elog_b[0:i])
# print Elog_beta
# print Elog_beta
return Elog_beta
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