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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| Format: | Article |
| Language: | English |
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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 |
| Summary: | 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. |
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| ISSN: | 1561-4042 |