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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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24 changes: 24 additions & 0 deletions sympy/functions/special/tests/test_zeta_functions.py
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Original file line number Diff line number Diff line change
Expand Up @@ -229,6 +229,30 @@ def test_lerchphi_expansion():
assert myexpand(lerchphi(exp(I*pi*Rational(2, 5)), s, a), None)


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 None
assert lerchphi(2, 1, 0).is_finite is False
assert lerchphi(2, -1, 0).is_finite is True
assert lerchphi(2, 1j, 0).is_finite is None
assert lerchphi(z, s, -1).is_finite is None
assert lerchphi(0, s, -1).is_finite is True
assert lerchphi(z, -3, 0).is_finite is True
assert lerchphi(0, s, 0).is_finite is None
assert lerchphi(0, 1, 0).is_finite is False
assert lerchphi(0, -1, 0).is_finite is True
assert lerchphi(0.5, -1, 0).is_finite is True
assert lerchphi(0.5+0.5j, 0, 0).is_finite is True
assert lerchphi(1, 3, 0).is_finite is False


def test_lerchphi_leadterm():
from sympy.functions.special.gamma_functions import digamma
assert (lerchphi(1-x, 1, a)._eval_as_leading_term(x)
== -log(x) - S.EulerGamma - digamma(a))


def test_stieltjes():
assert isinstance(stieltjes(x), stieltjes)
assert isinstance(stieltjes(x, a), stieltjes)
Expand Down
19 changes: 19 additions & 0 deletions sympy/functions/special/zeta_functions.py
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Expand Up @@ -214,6 +214,25 @@ 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.is_infinite or s.is_infinite or a.is_infinite:
# TODO: Write a valid implementation for infinite numbers.
return
if z == 0:
if a.is_zero is False:
return True
if s.is_real:
return s.is_nonpositive
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return
if a.is_integer and a.is_nonpositive:
if s.is_real:
return s.is_nonpositive
return
exp_expr = self.expand(func=True)
if exp_expr != self:
return exp_expr.is_finite
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What is expand(func=True) being used for here?

We should avoid creating new expressions during an assumptions query. Just creating the new expression runs the risk of triggering an identical assumptions query which leads to infinite recursion.

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Ok, I did not think about that. My idea was that, since LerchPhi includes a lot of common functions as particular values (zeta function, polylog, Dirichlet eta, ...), I can try to write the function in terms of these other functions and then let them determine whether the function is finite or not. Is there a safe way to do it without the risks you are mentioning?

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There is not really a safe way to do it. We just have to accept that the core assumptions cannot resolve all queries:
https://docs.sympy.org/latest/guides/assumptions.html

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Ok, sorry for the delay, but I haven't had time these last few weeks. I understand then that this part of the code should be changed and all the checks need to be implemented from scratch. Is that correct?

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Yes, the checks need to be from scratch. It is also acceptable that some assumptions queries just return None.


###############################################################################
###################### POLYLOGARITHM ##########################################
###############################################################################
Expand Down
4 changes: 4 additions & 0 deletions sympy/integrals/tests/test_integrals.py
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Expand Up @@ -2139,3 +2139,7 @@ def test_old_issues():
# https://github.com/sympy/sympy/issues/6278
I3 = integrate(1/(cos(x)+2),(x,0,2*pi))
assert I3 == 2*sqrt(3)*pi/3

def test_issue_26523():
Int = Integral((1 - t**z) / (1 - t), (t, 0, 1))
assert Int.doit() == polygamma(0, z + 1) + EulerGamma
17 changes: 16 additions & 1 deletion sympy/series/tests/test_limits.py
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Expand Up @@ -19,7 +19,8 @@
atan, cos, cot, csc, sec, sin, tan)
from sympy.functions.special.bessel import (besseli, bessely, besselj, besselk)
from sympy.functions.special.error_functions import (Ei, erf, erfc, erfi, fresnelc, fresnels)
from sympy.functions.special.gamma_functions import (digamma, gamma, uppergamma)
from sympy.functions.special.gamma_functions import (digamma, gamma, polygamma, uppergamma)
from sympy.functions.special.zeta_functions import lerchphi
from sympy.functions.special.hyper import meijerg
from sympy.integrals.integrals import (Integral, integrate)
from sympy.series.limits import (Limit, limit)
Expand Down Expand Up @@ -311,8 +312,11 @@ def test_set_signs():

def test_heuristic():
x = Symbol("x", real=True)
a = Symbol("a")
assert heuristics(sin(1/x) + atan(x), x, 0, '+') == AccumBounds(-1, 1)
assert limit(log(2 + sqrt(atan(x))*sqrt(sin(1/x))), x, 0) == log(2)
# https://github.com/sympy/sympy/issues/26523
assert heuristics(lerchphi(x, 1, a), x, 1, '-') != lerchphi(1, 1, a)


def test_issue_3871():
Expand Down Expand Up @@ -1412,3 +1416,14 @@ def test_issue_26250():
e1 = ((1-3*x**2)*e**2/2 - (x**2-2*x+1)*e*k/2)
e2 = pi**2*(x**8 - 2*x**7 - x**6 + 4*x**5 - x**4 - 2*x**3 + x**2)
assert limit(e1/e2, x, 0) == -S(1)/8


def test_issue_26523():
expr = -x**(z + 1)*lerchphi(x, 1, z + 1) - log(x - 1)
L = Limit(expr, x, 1, '-')
assert L.doit() == polygamma(0, z + 1) + EulerGamma - I*pi
expr = (-x*x**z*z*lerchphi(x, 1, z + 1)*gamma(z + 1)/gamma(z + 2)
- x*x**z*lerchphi(x, 1, z + 1)*gamma(z + 1)/gamma(z + 2)
- log(x - 1))
L = Limit(expr, x, 1, '-')
assert L.doit() == polygamma(0, z + 1) + EulerGamma - I*pi
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