AngouriMath
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OfAnErrorOrIntegralFunction(AngouriMath.Entity,AngouriMath.Entity,AngouriMath.Entity.Variable,AngouriMath.Entity,AngouriMath.Core.ApproachFrom)
Method (no overloads)
Summary
The limit of an error function or an exponential or trigonometric integral, given its
argument's limit: the value it tends to at an infinity, and the function of a finite limit
where it is continuous there.
argument's limit: the value it tends to at an infinity, and the function of a finite limit
where it is continuous there.
Remarks
None of these had a limit at all, so erf(x) at +oo, which is 1, was left unevaluated, and
so was erf(x) at 1. A logarithm of something holding one came to a stop that took more than
forty seconds: log(x + pi + erf(x), x^2 + tanh(1)) at +oo, which is 2. At an infinity:
erf to 1 and -1, erfc to 0 and 2, erfi, Shi to +oo and -oo, Si to pi/2 and -pi/2, Ci to 0,
Chi and li to +oo, and Ei to +oo and 0. Erf, erfc, erfi, Si and Shi are entire, so a finite
limit is put in as it is. Ci, Chi, Ei and li have a logarithm's singularity at 0 and its cut
below it, and li another at 1, so only a positive real limit other than li's 1 is put in;
elsewhere nothing is claimed. Each value at an infinity was checked against mpmath at 10^6 and
-10^6, and at 50 and -50 for erfi, Shi and Chi.
so was erf(x) at 1. A logarithm of something holding one came to a stop that took more than
forty seconds: log(x + pi + erf(x), x^2 + tanh(1)) at +oo, which is 2. At an infinity:
erf to 1 and -1, erfc to 0 and 2, erfi, Shi to +oo and -oo, Si to pi/2 and -pi/2, Ci to 0,
Chi and li to +oo, and Ei to +oo and 0. Erf, erfc, erfi, Si and Shi are entire, so a finite
limit is put in as it is. Ci, Chi, Ei and li have a logarithm's singularity at 0 and its cut
below it, and li another at 1, so only a positive real limit other than li's 1 is put in;
elsewhere nothing is claimed. Each value at an infinity was checked against mpmath at 10^6 and
-10^6, and at 50 and -50 for erfi, Shi and Chi.
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