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Give the error functions and the exponential and trigonometric integrals limits - #2373
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Rafael-SOWNet merged 1 commit intoNov 5, 2026
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…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>
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## master #2373 +/- ##
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- Coverage 86.76% 86.76% -0.01%
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Files 312 312
Lines 68911 68953 +42
Branches 20082 20096 +14
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+ Hits 59792 59828 +36
Misses 4921 4921
- Partials 4198 4204 +6
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November 5, 2026 17:56
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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.
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