## 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…

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 $\pi^m$.

$q$-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…

## References

SHOWING 1-10 OF 41 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…

CUBIC MODULAR EQUATIONS AND NEW RAMANUJAN-TYPE SERIES FOR $1/\pi$ : TALK GIVEN AT THE CONFERENCE "TOPICS IN NUMBER THEORY AND ITS APPLICATIONS", RIMS, KYOTO (Number Theory and its Applications)

- Mathematics
- 1998

In this paper, we derive new Ramanujan-type series for 1/π which belong to " Ramanujan's theory of elliptic functions to alternative base 3 " developed recently

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

- Mathematics
- 2008

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.