Fix hurwitz_zeta(0, x) not expanding

[pluschny]

Having defined:

def B(n, x):
    return -n*hurwitz_zeta(1 - n, x) if n != 0 else 1

we expect expand(B(n, x)) to match bernoulli_polynomial(x, n).

Using this small utility function to compare them:

def table(nmax):
    nab = [('n', 'expand(B(n, x))', 'bernoulli_polynomial(x, n)')]
    nab.extend([(n, expand(B(n, x)), bernoulli_polynomial(x, n))
                for n in range(nmax + 1)])
    k = len(str(nmax))
    m = max(len(str(x)) for t in nab for x in t)
    hline = '-' * (k + m + 7)
    print(hline)
    for n, a, b in nab:
        print(f' %{k}s     %{m}s' % (n, a))
        print(f' %{k}s     %{m}s' % ('', b))
        print(hline)

we notice they match except for n = 1:

sage: table(4)
----------------------------------
 n                expand(B(n, x))
       bernoulli_polynomial(x, n)
----------------------------------
 0                              1
                                1
----------------------------------
 1            -hurwitz_zeta(0, x)
                          x - 1/2
----------------------------------
 2                  x^2 - x + 1/6
                    x^2 - x + 1/6
----------------------------------
 3          x^3 - 3/2*x^2 + 1/2*x
            x^3 - 3/2*x^2 + 1/2*x
----------------------------------
 4       x^4 - 2*x^3 + x^2 - 1/30
         x^4 - 2*x^3 + x^2 - 1/30
----------------------------------

This ticket fixes that case.

[chapoton]

fixed, please review

---

New commits:

​785b4e2

Hurwitz zeta at n=0

[pluschny]

Looks good to me. Merci!

[chapoton]

reviewer full name please

[pluschny]

I don't know if I am qualified as a reviewer in the sense of the SageMath organization.

[slelievre]

I don't know if I am qualified as a reviewer in the sense of the SageMath organization.

You are!