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zeta(-1) returns 1/12 instead of -1/12 #3060

Closed rtoy closed 1 week ago

rtoy commented 1 week ago

Imported from SourceForge on 2024-07-07 12:41:17 Created by *anonymous on 2004-04-26 12:09:28 Original: https://sourceforge.net/p/maxima/bugs/564

The Riemann zeta function at -1 takes the value -1/12 (see (69) in http://mathworld.wolfram.com/RiemannZetaFunction.html, or use Cauchy's residue theorem on the representation of zeta(z) as an integral around the Hankel contour). However, in maxima, the call zeta(-1) returns 1/12.

Thanks,

Jamie Walker jamie@sagaxis.co.uk

rtoy commented 1 week ago

Imported from SourceForge on 2024-07-07 12:41:18 Created by willisbl on 2004-04-26 17:48:49 Original: https://sourceforge.net/p/maxima/bugs/564/#be83

fix for zeta function

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rtoy commented 1 week ago

Imported from SourceForge on 2024-07-07 12:41:22 Created by willisbl on 2004-04-26 17:48:49 Original: https://sourceforge.net/p/maxima/bugs/564/#471f

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Attached is a fix for zeta. The code could be improved in several ways. For one, zeta should simplify instead of evaluate. Also zeta should work for floating point arguments.

Barton

rtoy commented 1 week ago

Imported from SourceForge on 2024-07-07 12:41:25 Created by willisbl on 2004-04-27 13:19:13 Original: https://sourceforge.net/p/maxima/bugs/564/#92a1

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I've attached tests for the zeta function.

Barton

rtoy commented 1 week ago

Imported from SourceForge on 2024-07-07 12:41:29 Created by robert_dodier on 2004-12-31 19:37:54 Original: https://sourceforge.net/p/maxima/bugs/564/#2a92

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Footnote -- There are also two implementations of the zeta fcn, bzeta and bfzeta, in share/numeric/bffac.mac. These return bfloat (big float) values.

bzeta(-1,10) and bfzeta(-1,10) both return - 8.333333333333333B-2 which is -1/12 as a bfloat.

The description of bzeta in doc/info/Number.texi states that bzeta is obsolete and bfzeta should be used instead.

rtoy commented 1 week ago

Imported from SourceForge on 2024-07-07 12:41:32 Created by robert_dodier on 2006-07-05 23:21:17 Original: https://sourceforge.net/p/maxima/bugs/564/#f804

rtoy commented 1 week ago

Imported from SourceForge on 2024-07-07 12:41:36 Created by robert_dodier on 2006-07-05 23:21:17 Original: https://sourceforge.net/p/maxima/bugs/564/#09e4

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Fixed by r1.11 src/combin.lisp. The test script was committed as tests/rtest_zeta.mac. Closing this report as fixed.