### Abstract

In 1812, Gauss obtained fifteen contiguous functions relations. Later on, 1847, Henie gave their q-analogue. Recently, good progress has been done in finding more contiguous functions relations by employing results due to Gauss. In 1999, Cho et al. have obtained 24 new and interesting contiguous functions relations with the help of Gauss's 15 contiguous relations. In fact, such type of 72 relations exists and therefore the rest 48 contiguous functions relations have very recently been obtained by Rakha et al.. Thus, the paper is in continuation of the paper [16] published in Computer & Mathematics with Applications 61 (2011), 620-629. In this paper, first we obtained 15 q-contiguous functions relations due to Henie by following a different method and then with the help of these 15 q-contiguous functions relations, we obtain 72 new and interesting qcontiguous functions relations. These q-contiguous functions relations have wide applications.

Original language | English |
---|---|

Pages (from-to) | 65-94 |

Number of pages | 30 |

Journal | Communications of the Korean Mathematical Society |

Volume | 31 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2016 |

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### Keywords

- Basic hypergeometric series
- Gauss's contiguous functions relations
- Q-contiguous functions relations

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications of the Korean Mathematical Society*,

*31*(1), 65-94. https://doi.org/10.4134/CKMS.2016.31.1.065

**A study of q-contiguous function relations.** / Harsh, Harsh Vardhan; Kim, Yong Sup; Rakha, Medhat Ahmed; Rathie, Arjun Kumar.

Research output: Contribution to journal › Article

*Communications of the Korean Mathematical Society*, vol. 31, no. 1, pp. 65-94. https://doi.org/10.4134/CKMS.2016.31.1.065

}

TY - JOUR

T1 - A study of q-contiguous function relations

AU - Harsh, Harsh Vardhan

AU - Kim, Yong Sup

AU - Rakha, Medhat Ahmed

AU - Rathie, Arjun Kumar

PY - 2016

Y1 - 2016

N2 - In 1812, Gauss obtained fifteen contiguous functions relations. Later on, 1847, Henie gave their q-analogue. Recently, good progress has been done in finding more contiguous functions relations by employing results due to Gauss. In 1999, Cho et al. have obtained 24 new and interesting contiguous functions relations with the help of Gauss's 15 contiguous relations. In fact, such type of 72 relations exists and therefore the rest 48 contiguous functions relations have very recently been obtained by Rakha et al.. Thus, the paper is in continuation of the paper [16] published in Computer & Mathematics with Applications 61 (2011), 620-629. In this paper, first we obtained 15 q-contiguous functions relations due to Henie by following a different method and then with the help of these 15 q-contiguous functions relations, we obtain 72 new and interesting qcontiguous functions relations. These q-contiguous functions relations have wide applications.

AB - In 1812, Gauss obtained fifteen contiguous functions relations. Later on, 1847, Henie gave their q-analogue. Recently, good progress has been done in finding more contiguous functions relations by employing results due to Gauss. In 1999, Cho et al. have obtained 24 new and interesting contiguous functions relations with the help of Gauss's 15 contiguous relations. In fact, such type of 72 relations exists and therefore the rest 48 contiguous functions relations have very recently been obtained by Rakha et al.. Thus, the paper is in continuation of the paper [16] published in Computer & Mathematics with Applications 61 (2011), 620-629. In this paper, first we obtained 15 q-contiguous functions relations due to Henie by following a different method and then with the help of these 15 q-contiguous functions relations, we obtain 72 new and interesting qcontiguous functions relations. These q-contiguous functions relations have wide applications.

KW - Basic hypergeometric series

KW - Gauss's contiguous functions relations

KW - Q-contiguous functions relations

UR - http://www.scopus.com/inward/record.url?scp=84957624512&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957624512&partnerID=8YFLogxK

U2 - 10.4134/CKMS.2016.31.1.065

DO - 10.4134/CKMS.2016.31.1.065

M3 - Article

VL - 31

SP - 65

EP - 94

JO - Communications of the Korean Mathematical Society

JF - Communications of the Korean Mathematical Society

SN - 1225-1763

IS - 1

ER -