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Fix digamma integral #26563

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Fix digamma integral #26563

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56290f8
Add regression tests
rogerbalsach May 4, 2024
c1db033
Implement LerchPhi.is_finite
rogerbalsach May 4, 2024
aa567b2
Fixed bugs with LerchPhi.is_finite
rogerbalsach May 4, 2024
03693d9
Remove expand and fix bug.
rogerbalsach May 28, 2024
85de79f
Implemented lerchphi._eval_as_leading_term
rogerbalsach May 29, 2024
2fa2b3d
Fixed lerchphi._eval_a_leading_term
rogerbalsach Jun 12, 2024
7adec8d
Fixed lerchphi translation to Mathematica
rogerbalsach Jun 14, 2024
24e64b1
Fix import lerchphi in test_mathematica.
rogerbalsach Jun 14, 2024
e98fdd4
Modified heuristics function
rogerbalsach Jun 15, 2024
1274f58
Added gammasimp in limit function.
rogerbalsach Jun 15, 2024
9eb64e4
Add author
rogerbalsach Jun 15, 2024
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4 changes: 4 additions & 0 deletions sympy/functions/special/tests/test_zeta_functions.py
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Expand Up @@ -231,6 +231,10 @@ def test_lerchphi_expansion():

def test_lerchphi_finite():
assert lerchphi(1, 1, a).is_finite is False
assert lerchphi(0, -3, 0).is_finite is True
assert lerchphi(2, s, 0).is_finite is False
assert lerchphi(z, s, -1).is_finite is False
assert lerchphi(z, s, -5).is_finite is False


def test_lerchphi_leadterm():
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10 changes: 10 additions & 0 deletions sympy/functions/special/zeta_functions.py
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Expand Up @@ -214,6 +214,16 @@ def _eval_rewrite_as_zeta(self, z, s, a, **kwargs):
def _eval_rewrite_as_polylog(self, z, s, a, **kwargs):
return self._eval_rewrite_helper(polylog)

def _eval_is_finite(self):
z, s, a = self.args
if z == 0 or a == 0:
return z.is_zero and a.is_zero and s.is_nonpositive
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What should happen here if any of the is_ checks gives None?

https://docs.sympy.org/latest/guides/booleans.html

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Hi @oscarbenjamin , thanks for taking a look and the information about the booleans.
I thought python and was compatible with the fuzzy logic but it is indeed not. I will use the fuzzy_and function, this should handle correctly the None cases.
Also, I am not sure what is the convention when the function evaluates to NaN, should the is_finite be None?

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what is the convention when the function evaluates to NaN, should the is_finite be None?

Probably. What case evaluates to nan that you are thinking of?

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It is because a lot of situations where the function is infinite is because one has $0^{-s}$. The previous check s.is_nonpositive gives False when s is not real. I have added a check for s to be real, when s is complex the expression is undefined so now the function should return None.

if z == 1:
# Let zeta handle this case
return self._eval_expand_func().is_finite
if a.is_integer and a.is_nonpositive:
return False

###############################################################################
###################### POLYLOGARITHM ##########################################
###############################################################################
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