Abstract
In the theory of hypergeometric and generalized hypergeometric series, classical summation theorems have been found interesting applications in obtaining various series identities for π, π2 and 1 / π. The aim of this research paper is to provide twelve general formulas for 1 / π. On specializing the parameters, a large number of very interesting series identities for 1 / π not previously appeared in the literature have been obtained. Also, several other results for multiples of π, π2, 1 π / 2, 1 π / 3 and 1 √ π have been obtained. The results are established with the help of the extensions of classical Gauss's summation theorem available in the literature.
| Original language | English |
|---|---|
| Pages (from-to) | 865-874 |
| Number of pages | 10 |
| Journal | Communications of the Korean Mathematical Society |
| Volume | 32 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2017 |
| Externally published | Yes |
Keywords
- Hypergeometric summation theorems
- Ramanujan series for 1 / π
- Watson's theorem
- Whipple's theorem
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics