## A new method to obtain series for $$1/\pi$$ and $$1/\pi^2$$.(English)Zbl 1113.11076

The author conjectures several Ramanujan-type series for $$1/\pi$$ and for $$1/\pi^2$$. As evidence supporting their validity he presents several examples that have been checked numerically with a precision of 200 digits. For example, $\sum_ {n=0}^ \infty\sum_ {j=0}^ n "\begin{pmatrix} 2j\\ j\end{pmatrix}^ 2 \begin{pmatrix} 2n-2j\\ n-j\end{pmatrix}^ 2\left(\frac{2-\sqrt{3}}{64}\right)^ n \left(\frac{1}{4}+\frac{3+2\sqrt{3}}{4}n\right)=\frac{1}{\pi}.$

### MSC:

 11Y60 Evaluation of number-theoretic constants 33C20 Generalized hypergeometric series, $${}_pF_q$$

### Keywords:

Ramanujan-type series
Full Text:

### Online Encyclopedia of Integer Sequences:

Decimal expansion of 1/Pi.