Iteration limit exceeded evaluating N[Hypergeometric1F1[...]]

[bdlucas1]

Description

In[1]:= N[Hypergeometric1F1[a, b, (x + I y)^2]]
$IterationLimit::itlim: Iteration limit of 4096 exceeded.
Out[1]= $Aborted

but some variants substituting numerical values for some of a, b, x, y succeed. For example the following succeed:

N[Hypergeometric1F1[1, b, (x + I y)^2]] (* substitute 1 for a *)
N[Hypergeometric1F1[a, b, (x + I 1)^2]] (* substitute 1 for y *)

However the following still fails

N[Hypergeometric1F1[a, 1, (x + I y)^2]] (* substitute 1 for b *)

How to Reproduce

See description

Output Given

See description

Expected behavior

Return a result without exceeding iteration limit

Your Environment

MacOS

Mathics3 9.0.0
on CPython 3.12.10 (main, Apr 8 2025, 11:35:47) [Clang 16.0.0 (clang-1600.0.26.6)]
using SymPy 1.13.3, mpmath 1.3.0, numpy 2.3.2, cython Not installed

Workarounds

None known

Priority

Additional context

Discovered as a test case while investigating strategies for implementing things like ComplexPlot3D and Manipulate.

[rocky]

For what it's worth, Mathemathica returns the result with N[] stripped off: Hypergeometric1F1[a, b, (x + I y)^2]]. It doesn't give an iteration limit timeout, though.

This might be what Mathematica does when it can't evaluate a function.

[rocky]

It looks like we're looping in rewrite or evaluation somewhere. Should be pretty straightforward to fix.

[bdlucas1]

For what it's worth, Mathemathica returns the result with N[] stripped off: Hypergeometric1F1[a, b, (x + I y)^2]]. It doesn't give an iteration limit timeout, though.

This might be what Mathematica does when it can't evaluate a function.

Yes, that's what I would expect since no simplification or numerical evaluation is possible. I should have mentioned the context: this occurs when calling compile_quiet_function from plot.py on Hypergeometric1F1[a, b, (x + I y)^2]], both with has_compile = True or False, because in both cases I think it evaluates N[...] before or as part of compiling.

Also occurs when you do Compile[{a,b,x,y}, N[Hypergeometric1F1[a, b, (x + I y)^2]]], which I think is more-or-less equivalent to calling compile_quiet_function with has_compile = True.