Ramanujan-like formulas for 1/π2 a la Guillera and Zudilin and Calabi-Yau differential equations
Using the PSLQ-algorithm J.Guillera found some formulas for 1/π2. He proved three of them using WZ-pairs. Then W. Zudilin showed how to produce formulas for 1/π2 by squaring formulas for 1/π. The success of this depends on facts related to Calabi-Yau differential equations of string theory. Here som...
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Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova
2009-06-01
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| Series: | Computer Science Journal of Moldova |
| Online Access: | http://www.math.md/files/csjm/v17-n1/v17-n1-(pp-100-120).pdf |
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doaj-5c5c3f0a900f4828b98c4ecd909cfb2d2020-11-24T21:09:52ZengInstitute of Mathematics and Computer Science of the Academy of Sciences of MoldovaComputer Science Journal of Moldova1561-40422009-06-01171(49)100120Ramanujan-like formulas for 1/π2 a la Guillera and Zudilin and Calabi-Yau differential equationsGert Almkvist0Lund University, Department of Mathematics, P.O. Box 118 S-221 00 Lund, SwedenUsing the PSLQ-algorithm J.Guillera found some formulas for 1/π2. He proved three of them using WZ-pairs. Then W. Zudilin showed how to produce formulas for 1/π2 by squaring formulas for 1/π. The success of this depends on facts related to Calabi-Yau differential equations of string theory. Here some examples of this is worked out. Also some formulas containing harmonic numbers are found by differentiating formulas for 1/π2.http://www.math.md/files/csjm/v17-n1/v17-n1-(pp-100-120).pdf |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Gert Almkvist |
| spellingShingle |
Gert Almkvist Ramanujan-like formulas for 1/π2 a la Guillera and Zudilin and Calabi-Yau differential equations Computer Science Journal of Moldova |
| author_facet |
Gert Almkvist |
| author_sort |
Gert Almkvist |
| title |
Ramanujan-like formulas for 1/π2 a la Guillera and Zudilin and Calabi-Yau differential equations |
| title_short |
Ramanujan-like formulas for 1/π2 a la Guillera and Zudilin and Calabi-Yau differential equations |
| title_full |
Ramanujan-like formulas for 1/π2 a la Guillera and Zudilin and Calabi-Yau differential equations |
| title_fullStr |
Ramanujan-like formulas for 1/π2 a la Guillera and Zudilin and Calabi-Yau differential equations |
| title_full_unstemmed |
Ramanujan-like formulas for 1/π2 a la Guillera and Zudilin and Calabi-Yau differential equations |
| title_sort |
ramanujan-like formulas for 1/π2 a la guillera and zudilin and calabi-yau differential equations |
| publisher |
Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova |
| series |
Computer Science Journal of Moldova |
| issn |
1561-4042 |
| publishDate |
2009-06-01 |
| description |
Using the PSLQ-algorithm J.Guillera found some formulas for 1/π2. He proved three of them using WZ-pairs. Then W. Zudilin showed how to produce formulas for 1/π2 by squaring formulas for 1/π. The success of this depends on facts related to Calabi-Yau differential equations of string theory. Here some examples of this is worked out. Also some formulas containing harmonic numbers are found by differentiating formulas for 1/π2. |
| url |
http://www.math.md/files/csjm/v17-n1/v17-n1-(pp-100-120).pdf |
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AT gertalmkvist ramanujanlikeformulasfor1p2alaguilleraandzudilinandcalabiyaudifferentialequations |
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