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Consistent evaluation of Tricomi U(a,b,z)#92

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Consistent evaluation of Tricomi U(a,b,z)#92
AshtonSBradley wants to merge 2 commits intoJuliaMath:masterfrom
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@AshtonSBradley AshtonSBradley commented Apr 12, 2026

This resolves #61 , #63, adding tests from #63, and additional tests to increase PR coverage.

Reworked U(a,b,z) in src/confluent.jl (line 42) so it no longer relies on the large-|z| asymptotic formula for every case. The new implementation uses the exact DLMF connection formula for noninteger b, the integer-b series from DLMF 13.2.9, Kummer’s transformation for nonpositive integer b, and a polynomial path when a is a nonpositive integer. Direct U(1,1,z) evaluation also added for stability.

The regression tests in test/runtests.jl (line 603) now cover the negative-real-axis cases from issue #63 plus the real-negative input behaviour that used to throw. Pkg.test() passes.

The key formulas used were DLMF 13.2.42, 13.2.9, and Kummer’s transformation as noted in issue #61.

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codecov bot commented Apr 12, 2026

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 85.17%. Comparing base (1bea052) to head (b930925).

Additional details and impacted files
@@            Coverage Diff             @@
##           master      #92      +/-   ##
==========================================
+ Coverage   84.89%   85.17%   +0.27%     
==========================================
  Files           7        7              
  Lines        1470     1511      +41     
==========================================
+ Hits         1248     1287      +39     
- Misses        222      224       +2     

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@AshtonSBradley AshtonSBradley changed the title resolve #61 , adding tests from #63 Consistent evaluation of U(a,b,z) Apr 14, 2026
@AshtonSBradley AshtonSBradley changed the title Consistent evaluation of U(a,b,z) Consistent evaluation of Tricomi U(a,b,z) Apr 14, 2026
@MikaelSlevinsky
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Thanks for this @AshtonSBradley!

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Tricomi U small argument

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