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Give the error functions and the exponential and trigonometric integrals limits - #2373

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Nov 5, 2026
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Rafael-SOWNet merged 1 commit into
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erf, erfc, erfi, Si, Ci, Shi, Chi, Ei and li had no limit at all: even
erf(x) at +oo, which is 1, and erf(x) at 1 were left unevaluated, on
master and on 2.6.0.

At an infinity each now gives its known value (erf to +-1, erfc to 0 and
2, Si to +-pi/2, Ci to 0, Ei to +oo and 0; erfi, Shi, Chi and li to
+-oo), each checked with mpmath at +-10^6, or +-50 for erfi, Shi and Chi.
At a finite point the limit is the function of the argument's limit,
kept exact. erf, erfc, erfi, Si and Shi are entire, so any finite point
is accepted; Ci, Chi, Ei and li are singular at 0 and cut below it, so
only a positive real point is, and li also excludes 1. Nothing is
claimed on a cut.

The limitcheck A/B over 24 seeds decides 30 to 290 more limits per seed,
with no value lost. The new two-sided NaNs are 0^0 forms such as
erf(x)^x at 0, which follow the x^x convention; their one-sided limits
are right. 16 of the 19 new test rows fail on master.

🤖 Generated with Claude Code

…als limits

erf, erfc, erfi, Si, Ci, Shi, Chi, Ei and li had no limit at all: even
erf(x) at +oo, which is 1, and erf(x) at 1 were left unevaluated, on
master and on 2.6.0.

At an infinity each now gives its known value (erf to +-1, erfc to 0 and
2, Si to +-pi/2, Ci to 0, Ei to +oo and 0; erfi, Shi, Chi and li to
+-oo), each checked with mpmath at +-10^6, or +-50 for erfi, Shi and Chi.
At a finite point the limit is the function of the argument's limit,
kept exact. erf, erfc, erfi, Si and Shi are entire, so any finite point
is accepted; Ci, Chi, Ei and li are singular at 0 and cut below it, so
only a positive real point is, and li also excludes 1. Nothing is
claimed on a cut.

The limitcheck A/B over 24 seeds decides 30 to 290 more limits per seed,
with no value lost. The new two-sided NaNs are 0^0 forms such as
erf(x)^x at 0, which follow the x^x convention; their one-sided limits
are right. 16 of the 19 new test rows fail on master.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
@Rafael-SOWNet Rafael-SOWNet added this to the 2.7.0 milestone Nov 4, 2026
@Rafael-SOWNet Rafael-SOWNet moved this from Todo to In review in AngouriMath Nov 4, 2026
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codecov Bot commented Nov 4, 2026 •

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Codecov Report

❌ Patch coverage is 71.42857% with 12 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.76%. Comparing base (eda9e03) to head (1423305).

Files with missing lines Patch % Lines
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs 71.42% 7 Missing and 5 partials ⚠️
Additional details and impacted files

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@@            Coverage Diff             @@
##           master    #2373      +/-   ##
==========================================
- Coverage   86.76%   86.76%   -0.01%     
==========================================
  Files         312      312              
  Lines       68911    68953      +42     
  Branches    20082    20096      +14     
==========================================
+ Hits        59792    59828      +36     
  Misses       4921     4921              
- Partials     4198     4204       +6     
Flag Coverage Δ
cpp 37.77% <ø> (ø)
csharp 87.30% <71.42%> (-0.01%) ⬇️
fsharp 32.97% <ø> (ø)
interactive 40.72% <ø> (ø)

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Files with missing lines Coverage Δ
...nctions/Continuous/Limits/Solvers/Limit.Classes.cs 74.41% <71.42%> (-0.43%) ⬇️

... and 6 files with indirect coverage changes

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@Rafael-SOWNet
Rafael-SOWNet merged commit 2d26789 into master Nov 5, 2026
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@github-project-automation github-project-automation Bot moved this from In review to Done in AngouriMath Nov 5, 2026
@Rafael-SOWNet
Rafael-SOWNet deleted the feature/limits-of-the-error-and-integral-functions branch November 5, 2026 17:56
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