A WZ proof of Ramanujan's Formula for Pi

We derive 10 new Ramanujan-Sato series of $1/\pi$ by using the method of Huber, Schultz and Ye. The levels of these series are 14, 15, 16, 20, 21, 22, 26, 35, 39.

This paper has been withdrawn

We prove rational alternating Ramanujan-type series of level $1$ discovered by the brothers David and Gregory Chudnovky, by using a method of the author. We have carried out the computations with Maple (a symbolic software for mathematics).

In 1914, Ramanujan presented a collection of 17 elegant and rapidly converging formulae for $\pi$. Among these, one of the most celebrated is the following series: \[\frac{1}{\pi}=\frac{2\sqrt{2}}{9801}\sum_{n=0}^{\infty}\frac{26390n+1103}{\left(n!\right)^4}\cdot \frac{\left(4n\right)!}{396^{4n}}\] In this paper, we give a proof of this classic formula using hypergeometric series and a special type of lattice sum due to Zucker and Robertson. In turn, we will also use some res...

In this short note, we aim to discuss some summations due to Ramanujan, their generalizations and some allied series

This short note delivers, via elementary calculations, a product representation of pi.

The Ramanujan Machine project detects new expressions related to constants of interest, such as $\zeta$ function values, $\gamma$ and algebraic numbers (to name a few). In particular the project lists a number of conjectures involving even and odd $\zeta$ function values, logarithms etc. We show that many relations detected by the Ramanujan Machine Project stem from a specific algebraic observation and show how to generate infinitely many. This provides an automated proof and...

In this article we give the theoretical background for generating Ramanujan type $1/\pi^{2\nu}$ formulas. As applications of our method we give a general construction of $1/\pi^4$ series and examples of $1/\pi^6$ series. We also study the elliptic alpha function whose values are useful for such evaluations.

This short note is a comment on a historical aspect of a famous formula dating from the 18th century.

In this short research note, we aim to establish an interesting extension of a summation due to Ramanujan.The result is derived with the help of an extension of Gauss's summation theorem available in the literature.