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

N1 - Publisher Copyright:
© 2016 Korean Mathematical Society.

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

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U2 - 10.4134/CKMS.2016.31.1.065

DO - 10.4134/CKMS.2016.31.1.065

M3 - Article

AN - SCOPUS:84957624512

SN - 1225-1763

VL - 31

SP - 65

EP - 94

JO - Communications of the Korean Mathematical Society

JF - Communications of the Korean Mathematical Society

IS - 1

ER -