A study of q-contiguous function relations
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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 \cite{Rakha} published in Computer \& Mathematics with Applications {\bf 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 q-contiguous functions relations. These q-contiguous functions relations have wide applications.
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 \cite{Rakha} published in Computer \& Mathematics with Applications {\bf 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 q-contiguous functions relations. These q-contiguous functions relations have wide applications.
참고문헌 (17)
- G. E. Andrews, "On the q-analog of Kummer’s theorem and applications", Duke Math. J, 40, pp.525~528 (1973)
- W. N. Bailey, "A note on certain q-identities", Quart. J. Math, 12, pp.173~175 (1941)
- Y. J. Cho, "Note on contiguous functions relations", East Asian Math. J, 15(1), pp.29~38 (1999)
- J. A. Dhaum, "The basic analog of Kummer’s theorems", Bull. Amer. Math. Soc, 8, pp.711~713 (1942)
- G. Gasper, "Basic hypergeometric series" (1990), Cambridge University Press
- C. F. Gauss, "Disquisitiones generales circa seriem infinitam", Comm. Soc. Reg. Sci. G¨ott. Rec., Vol. II; reprinted in Werke, 3, pp.123~162 (1876)
- E. Henie, "Untersuchungen uber die Rehie", J. Reine Angew. Math, 34, pp.285~328 (1847)
- A. K. Ibrahim, "Contiguous relations and their computations for 2F1hypergeometric series", Comput. Math. Appl, 56(8), pp.1918~1926 (2008)
- F. H. Jackson, "Transformation of q-series", Messenger of Math, 39, pp.145~153 (1910)
- Y. S. Kim, "Another method for proving a q-analogue of Gauss’s summation theorem", Far East J. Math. Sci, 5(3), pp.317~322 (2002)
- Yong Sup Kim, "Three-term contiguous functional relationsfor basic bypergeometric series ${}_2$", 대한수학회논문집, 20(2), pp.395~403 (2005), 대한수학회
- Yong Sup Kim, "On q-Analog of Kummer's Theorem And its Contiguous Results", 대한수학회논문집, 18(1), pp.151~157 (2003), 대한수학회
- W. Miller, Jr., "Lie theory and generalizations of hypergeometric functions", SIAM J. Appl. Math, 25, pp.226~235 (1973)
- E. D. Rainville, "The contiguous function relations for pFq with applications to Bate-man’s Ju,v n and Rice’s Hn(ζ, p, v)", Bull. Amer. Math. Soc, 51, pp.714~723 (1945)
- E. D. Rainville, "Special Functions" (1960), The Macmillan Company
- M. A. Rakha, "On contiguous function relations", Comput. Math. Appl, 61, pp.620~629 (2011)
- C. Wei, "q-Extensions of Gauss’ fifteen contiguous relation for 2F1 series", Commun. Computer Information Science, 105(2), pp.85~92 (2011)