## 7 Citations

### Ramanujan-type formulae for $1/\pi$: The art of translation

- Mathematics
- 2013

We outline an elementary method for proving numerical hypergeometric identities, in particular, Ramanujan-type identities for $1/\pi$. The principal idea is using algebraic transformations of…

### $q$-analogues of several $\pi $-formulas

- Physics, MathematicsProceedings of the American Mathematical Society
- 2020

According to the $q$-series method, a short proof for Hou and Sun's identity, which is the $q$-analogue of a known $\pi$-formula, is offered. Furthermore, $q$-analogues of several other…

### Extensions of the classical theorems for very well-poised hypergeometric functions

- Mathematics
- 2019

The well-known classical summation theorems due to Dougall and certain transformation formulas due to Whipple and Bailey for very well-poised hypergeometric functions are extended by introducing two…

### Pell's equation and series expansions for irrational numbers

- Mathematics
- 2016

Solutions of Pell's equation and hypergeometric series identities are used to study series expansions for $\sqrt{p}$ where $p$ are arbitrary prime numbers. Numerous fast convergent series expansions…

### Series expansions for $1/\pi^m$ and $\pi^m$

- Education
- 2013

By means of the telescoping method, we establish two sum- mation formulas on sine function. As the special cases of them, several interesting series expansions for $1/\pi^m$ and $\pi^m$.

## References

SHOWING 1-10 OF 39 REFERENCES

### Gauss summation and Ramanujan type series for $1/{\pi}$

- Mathematics
- 2012

Using some properties of the gamma function and the well-known Gauss summation formula for the classical hypergeometric series, we prove a four-parameter series expansion formula, which can produce…

### Ramanujan's series for 1/π arising from his cubic and quartic theories of elliptic functions

- Mathematics
- 2008

### Ramanujan-type formulae for 1/π: a second wind?

- Mathematics
- 2006

In 1914 S. Ramanujan recorded a list of 17 series for 1=…. We survey the methods of proofs of Ramanujan’s formulae and indicate recently discovered generalisations, some of which are not yet proven.…

### Hypergeometric identities for 10 extended Ramanujan-type series

- Mathematics
- 2008

We prove, by the WZ-method, some hypergeometric identities which relate ten extended Ramanujan type series to simpler hypergeometric series. The identities we are going to prove are valid for all the…

### Ramanujan's Class Invariant λn and a New Class of Series for 1/π

- Mathematics
- 2001

On page 212 of his lost notebook, Ramanujan defined a new class invariant λn and constructed a table of values for λn. The paper constructs a new class of series for 1/π associated with λn. The new…

### About a New Kind of Ramanujan-Type Series

- MathematicsExp. Math.
- 2003

A new kind of Ramanujan-type formula for 1/π is proposed and it is conjectured that it is related to the theory of modular functions.

### New 5F4 hypergeometric transformations, three-variable Mahler measures, and formulas for 1/π

- Mathematics
- 2007

Abstract
New relations are established between families of three-variable Mahler measures. Those identities are then expressed as transformations for the 5F4 hypergeometric function. We use these…

### Eisenstein series and Ramanujan-type series for 1/π

- Mathematics
- 2010

Using certain representations for Eisenstein series, we uniformly derive several Ramanujan-type series for 1/π.