josdejong/mathjs

lgammaNumber incorrectly returns NaN for all n < 0

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#3604 opened on Nov 27, 2025

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 (6 comments) (0 reactions) (0 assignees)JavaScript (13,832 stars) (1,298 forks)batch import
bugcategory:numericalhelp wanted

Description

Describe the bug

lgammaNumber incorrectly returns NaN for all n < 0.

To Reproduce

  1. Call mathjs.log(mathjs.gamma(-1.5)) and get 0.8600470153764809.
  2. Call mathjs.lgamma(-1.5) and get NaN.
  3. See that the returned values are not equal.

Problematic code

https://github.com/josdejong/mathjs/blob/4bbe862bb553bd765685b46d977e8ee226e4abf0/src/plain/number/probability.js#L91-L92

Suggested solution

Change the code

return NaN

to

Math.log(Math.PI / Math.sin(Math.PI * n)) - lgammaNumber(1 - n)

It correctly returns NaN for $n \in (-2k-1, -2k)$ and positive values for $n \in (-2k, -2k+1)$ for $k \in ℕ$.

You can check it for -1.5 too: Math.log(Math.PI / Math.sin(Math.PI * -1.5)) - mathjs.lgamma(1 - -1.5) returns 0.8600470153764859, which is close to 0.8600470153764809.

You can also just remove this if statement, because the one below already handles the n < 0 case properly: https://github.com/josdejong/mathjs/blob/4bbe862bb553bd765685b46d977e8ee226e4abf0/src/plain/number/probability.js#L96-L100

Contributor guide

Tech stack
javascript
Domain
api
Issue type
bug
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
1
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under 1 hour
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fresh
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clear
Prerequisites
None
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
90
Research direction
The issue describes a bug in the lgammaNumber function at src/plain/number/probability.js#L91 L92. The suggested fix replaces the return NaN with a formula using Math.log and Math.sin. The fix should be implemented and verified against the provided test case (lgamma( 1.5) should return ~0.8600470153764809). Also ensure that existing tests pass and consider adding new tests for negative non integer values.