Comment #2 on issue 3706 by [email protected]: Hyperexpand of tan
http://code.google.com/p/sympy/issues/detail?id=3706
We can get an answer by substituting the pi away:
In [67]: _.subs(pi, t)
Out[67]: 8*z*hyper((1, 1/2 - z/t, 1/2 + z/t), (3/2 - z/t, 3/2 + z/t),
1)/(t**2 - 4*z**2)
In [68]: hyperexpand(_)
Out[68]: 8*z*((-t**2 + 4*z**2)*lerchphi(1, 1, (t + 2*z)/(2*t))/(8*t*z) +
(t**2 - 4*z**2)*lerchphi(1, 1, (-t +
2*z)*exp_polar(I*pi)/(2*t))/(8*t*z))/(t**2 - 4*z**2)
In [69]: simplify(_)
Out[69]: (-lerchphi(1, 1, (t + 2*z)/(2*t)) + lerchphi(1, 1, (-t +
2*z)*exp_polar(I*pi)/(2*t)))/t
In [70]: _.subs(t, pi)
Out[70]: (-lerchphi(1, 1, (2*z + pi)/(2*pi)) + lerchphi(1, 1, (2*z -
pi)*exp_polar(I*pi)/(2*pi)))/pi
In [71]: simplify(_)
Out[71]: (-lerchphi(1, 1, (2*z + pi)/(2*pi)) + lerchphi(1, 1, (2*z -
pi)*exp_polar(I*pi)/(2*pi)))/pi
The solution however is not that useful, maybe not even correct:
In [82]: _.subs(z, 0)
Out[82]:
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
[...]
ValueError: gamma function pole
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