Ramanujan-like formulas for 1 ¼2 a la Guillera and Zudilin and Calabi-Yau differential equations
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517.9 (243)
Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (241)
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ALMKVIST, Gest. Ramanujan-like formulas for 1 ¼2 a la Guillera and Zudilin and Calabi-Yau differential equations. In: Computer Science Journal of Moldova, 2009, nr. 1(49), pp. 100-120. ISSN 1561-4042.
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Computer Science Journal of Moldova
Numărul 1(49) / 2009 / ISSN 1561-4042 /ISSNe 2587-4330

Ramanujan-like formulas for 1 ¼2 a la Guillera and Zudilin and Calabi-Yau differential equations
CZU: 517.9

Pag. 100-120

Almkvist Gest
 
Lund University, Sweden
 
Disponibil în IBN: 6 decembrie 2013


Rezumat

Using the PSLQ-algorithm J.Guillera found some formulas for 1 ¼2 . He proved three of them using WZ-pairs. Then W. Zudilin showed how to produce formulas for 1 ¼2 by squaring formulas for 1 ¼ . 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 di®erentiating formulas for 1 ¼2 .