[Maxima-bugs] [maxima:bugs] #5294 diff(struve_h(v, t), t) and diff(struve_l(v, t), t) contain x^v instead of t^v

[David S. <tom...@us...>]

- Description has changed:

Diff:

~~~~



~~~~

- **status**: open --> closed
- **Priority**:  --> 5
- **Comment**:

Fixed by commit [30638c].



---

**[bugs:#5294] diff\(struve\_h\(v,t\),t\) and diff\(struve\_l\(v,t\),t\) contain x^v instead of t^v**

**Status:** closed
**Group:** Includes\_proposed\_fix
**Labels:** Claude trivial bug bessel.lisp 
**Created:** Sun Sep 27, 2026 08:34 AM UTC by David Scherfgen
**Last Updated:** Sun Sep 27, 2026 12:31 PM UTC
**Owner:** nobody


This bug was discovered by Claude Opus 5.5 and reproduced on Maxima Git commit c62924c (2026-09-26) with SBCL 2.2.9.

**Where:** `src/bessel.lisp`, DEFGRAD %STRUVE\_H, DEFGRAD %STRUVE\_L

The derivative templates use x^v, but the DEFGRAD placeholders are $v and $z, so x is a literal free symbol instead of the argument. The result is only right when the variable happens to be named x; struve\_l has the same error.

### Steps

1. Verify that the existing behavior is incorrect: run the reproducer below; it gives the result under "Before the fix". Judge for yourself that this is wrong instead of relying on the ticket: where the bug allows it, try some related inputs of your own, or check the result another way, for example numerically or against the documentation.
2. Edit the file `src/bessel.lisp` as described under "Fix".
3. Rebuild Maxima.
4. Verify that the behavior is now correct: the reproducer gives the result under "Correct result". Judge for yourself that this is right, not only that it matches: where the bug allows it, try some related inputs of your own, including some that the fix should leave unchanged.
5. Add the test case(s) under "Test cases" to `tests/rtest16.mac`, just before the block "Leave this at the end of the file!" at its end.
6. Run the complete test suite, share tests included (`make check`, or `run_testsuite(share_tests=true);` in `./maxima-local`), and check that the change breaks no test. Failures that also occur without the change (a run on the unchanged build shows which) are pre-existing and can be ignored.
7. Add the line `* \#5294 diff(struve_h(v,t),t) and diff(struve_l(v,t),t) contain x^v instead of t^v` to `ChangeLog`, under "Bug fixes for numbered bugs:".
8. Commit the fix; a proposed Git commit message is under "Commit message".
9. Push the commit. Then set this ticket's status to "closed" and add a comment naming the commit, for example `Fixed by commit [1a2b3c].`, with the first six characters of the commit's SHA in the brackets (`git rev-parse HEAD | cut -c1-6` prints them). SourceForge links this to the commit.

### Reproducer

```
diff(struve_h(v,t),t);
```

Before the fix:

```
(x^v/(2^v*sqrt(%pi)*gamma(v+3/2))-struve_h(v+1,t)+struve_h(v-1,t))/2
```

Correct result:

```
(t^v/(2^v*sqrt(%pi)*gamma(v+3/2))-struve_h(v+1,t)+struve_h(v-1,t))/2
```

### Fix

In `src/bessel.lisp` (DEFGRAD %STRUVE\_H, search for "-struve\_h(v+1,z)+struve\_h(v-1,z))/2$"), replace

```
  #$$ (x^v/(2^v*sqrt(%pi)*gamma(v+3/2))-struve_h(v+1,z)+struve_h(v-1,z))/2$
```

with

```
  #$$ (z^v/(2^v*sqrt(%pi)*gamma(v+3/2))-struve_h(v+1,z)+struve_h(v-1,z))/2$
```

In `src/bessel.lisp` (DEFGRAD %STRUVE\_L, search for "+struve\_l(v+1,z)+struve\_l(v-1,z))/2$"), replace

```
  #$$ (x^v/(2^v*sqrt(%pi)*gamma(v+3/2))+struve_l(v+1,z)+struve_l(v-1,z))/2$
```

with

```
  #$$ (z^v/(2^v*sqrt(%pi)*gamma(v+3/2))+struve_l(v+1,z)+struve_l(v-1,z))/2$
```

### Test cases

Add these lines to `tests/rtest16.mac`, separated from the tests before them by two empty lines:

```
/* Bug #5294: "diff(struve_h(v,t),t) and diff(struve_l(v,t),t) contain x^v instead of t^v" */

diff(struve_h(v,t),t);
(t^v/(2^v*sqrt(%pi)*gamma(v+3/2))-struve_h(v+1,t)+struve_h(v-1,t))/2$

diff(struve_l(v,t),t);
(t^v/(2^v*sqrt(%pi)*gamma(v+3/2))+struve_l(v+1,t)+struve_l(v-1,t))/2$
```

### Commit message

```
bessel.lisp: fix derivatives of struve_h and struve_l

The derivative templates of struve_h and struve_l wrote the power term
as x^v, but the DEFGRAD placeholders are v and z, so x was a free symbol
instead of the argument. They now use z^v.

This fixes bug #5294.

Found and fixed by Claude Opus 5.5.
```


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