Ramanujan-like formulas for ½ π a la Guillera and Zudilin and Calabi-Yau differential equations

Using the PSLQ-algorithm J.Guillera found some formulas for ~2 . He proved three of them using WZ-pairs. Then W. Zudilin showed how to produce formulas for by squaring formulas for 1 . 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