Comment #10 on issue 1893 by ness...@googlemail.com: integrate(log(x) *
x**(k-1) * exp(-x) / gamma(k), (x, 0, oo)) hangs
http://code.google.com/p/sympy/issues/detail?id=1893
This mostly works in gsoc-3 (https://github.com/sympy/sympy/pull/543):
In [78]: a = Symbol('a', positive=True)
In [79]: integrate(exp(-x)*log(x)*x**a, (x, 0, oo), meijerg=True)
Out[79]:
2 ┌─ ⎛a + 1, a + 1 │
⎞ 2 ┌─ ⎛a + 1, a + 1 │ ⎞
Γ(a + 1) ⋅ ├─ ⎜ │ -1⎟ Γ(-a -
1) ⋅ ├─ ⎜ │ -1⎟
2╵ 2 ⎝a + 2, a + 2 │
⎠ 2╵ 2 ⎝a + 2, a + 2 │ ⎠
a⋅Γ(a)⋅polygamma(0, a) + Γ(a) - ────────────────────────────────── +
───────────────────────────────────
2 2
Γ(a +
2) Γ(-a)
In [80]: simplify(simplify(_))
Out[80]: (a⋅polygamma(0, a) + 1)⋅Γ(a)
In [81]: simplify(_79)
Out[81]:
(a⋅polygamma(0, a) + 1)⋅Γ(a + 2)
────────────────────────────────
a⋅(a + 1)
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