논문KCI 등재
A new summation formula for basic bilateral hypergeometric series by 2φ2-exponential operator technique
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In the present work by making use of q-exponential opera- tor technique of parameter augmentation, we have obtained a new sum- mation formula for 2φ2 basic bilateral hypergeometric series. We also discuss some interesting applications of our result and deduced some identities of q-gamma, q-beta functions and eta-functions.
Abstract
In the present work by making use of q-exponential opera- tor technique of parameter augmentation, we have obtained a new sum- mation formula for 2φ2 basic bilateral hypergeometric series. We also discuss some interesting applications of our result and deduced some identities of q-gamma, q-beta functions and eta-functions.
참고문헌 (33)
- G. E. Andrews, "On Ramanujan's Summations of 1Ψ1(a;b;z)", Proc. Amer. Math. Soc., 22, pp.552~553 (1969)
- G. E. Andrews, "On a transformation of bilateral series with applications", Proc. Amer. Math. Soc., 25, pp.554~558 (1970)
- G. E. Andrews, "A simple proof of Ramanujan's summation of the 1Ψ1", Aeqa. Math., 18, pp.333~337 (1978)
- G. E. Andrews, "Ramanujan's Lost Notebook, Part II" (2009), Springer
- R. Askey, "The q-gamma and q-beta functions", Applicable Anal, 8, pp.125~141 (1978)
- R. Askey, "Ramanujan's 1Ψ1 and formal Laurent series", Indian J. Math, 29, pp.101~105 (1987)
- B. C. Berndt, "Ramanujan's Notebooks II" (1991), Springer-Verlag
- B. C. Berndt, "Ramanujan's Notebooks III" (1991), Springer-Verlag
- B. C. Berndt, "Ramanujan's identities for eta functions", Math. Ann, 292(3), pp.561~573 (1992)
- S. Bhargava, "A basic bilateral series summation formula and its appli-cations", Integral Transform and Special Functions, 2(3), pp.165~184 (1994)
- S. H. Chan, "Ramanujan's famous 1 1 summation formula", J. Appl. Theory, 132, pp.149~153 (2005)
- W. Y.C. Chen, "Mathematical Essays in honor of Gian-Carlo Rota,Ch.Parameter augmentation for basic hypergeometric series, I", pp.111~129 (1998), Birkhaiser
- W. Y. C. Chen, "Parameter augmentation for basic hypergeometric series, II", J. Combin. Theory. Series A, 80, pp.175~195 (1997)
- CHEN Xiao-jing, "A Short Proof of Ramanujan's 1 1Formula", Journal of Mathematical Research and Exposition, 28(1), pp.46~48 (2008)
- S. Corteel, "Frobenius partitions and the combinatorics of Ramanujan's 1Ψ1 summation", J. Combin. Theory Ser. A, 97, pp.177~183 (2002)
- D. D. Somashekara, "Some eta function identities deducible from Ramanujan's 1Ψ1 Summation", J. Math. Anal. Appl, 176(2), pp.554~560 (1993)
- D. D. Somashekara, "On a New Summation Formula for 2Ψ2 Basic Bilateral Hypergeometric Series and Its Applications", Int. J. of Math. and Mathematical Sciences, 2011
- N. J. Fine, "Basic Hypergeometric Series and Applications", American Mathematical Society (1988)
- G. Gasper, "Basic Hypergeometric Series" (1990), Cambridge University Press
- W. Hahn, "Beitrage zur Theorie der Heineschen Reihen", Math. Nachr, 2, pp.340~379 (1949)
- G. H. Hardy, "Ramanujan" (1978), Chelsea
- G. H. Hardy, "Ramanujan" (1999), American Mathematical Society
- M. E. H. Ismail, "A simple proof of Ramanujan's 1Ψ1 sum", Proc. Amer. Math. Soc., 63, pp.185~186 (1977)
- F. H. Jackson, "On q-definite integrals", Quar.Jour.Pure and Applied Math, 41, pp.193~203 (1910)
- M. Jackson, "On Lerch's transcendent and the basic bilateral hypergeometric series 2Ψ2", J. London Math. Soc., 25, pp.189~196 (1950)
- Zhi-Guo Liu, "Some operator identities and q-series transformation formulas", Discrete Math, 265, pp.119~139 (2003)
- K. Mimachi, "A proof of Ramanujan's identity by use of loop integral", SIAM J. Math. Anal., 19, pp.1490~1493 (1988)
- S. Ramanujan, "Notebooks" (1957), Tata Institute of Fundamental Research
- S. Roman, "More on the umbral calculus, with Emphasis on the q-umbral calculus", J. Math.Anal.Appl, 107, pp.222~254 (1985)
- K. R. Vasuki, "On a 2Ψ2 Basic Bilateral Hypergeometric Series Summation Formula", Int. Math. Forum, 5(15), pp.745~753 (2010)
- K. Venkatachaliengar, "Development of Elliptic Functions According to Ramanujan", pp.1988
- A. J. Yee, "Combinatorial proof of Ramanujan's 1Ψ1 summation and the q-Gauss sum-mation", J. Combin. Theory Ser. A., 105, pp.63~77 (2004)
- Zhizheng Zhang, "Jun Wang Two operator identities and their applications to termi-nating basic hypergeometric series and q-integrals", J. Math. Anal. Appl, 312, pp.653~665 (2005)
관련 논문AI추천
A Q-analogue of hypergeometric series by Q-exponential functionsLAXMI MAJHI장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2025 · 제28권 제4호CERTAIN SUMMATION FORMULAS FOR HUMBERT’S DOUBLE HYPERGEOMETRIC SERIES Ψ2 AND Φ2최준상, Arjun Kumar Rathie대한수학회 · 대한수학회논문집2015 · 제30권 제4호SOME APPLICATIONS OF q-DIFFERENTIAL OPERATORJian-Ping Fang대한수학회 · 대한수학회지2010 · 제47권 제2호On a q-Extension of the Leibniz Rule via Weyl Type of q-Derivative OperatorSunil Dutt Purohit경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제4호On certain transformations of basic hypergeometric functionsR. Y. Denis, S. N. Singh, S. P. Singh장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2007 · 제10권 제2호On Certain Continued Fractions Related To 3ψ3 Basic Bilateral Hypergeometric FunctionsAbdulrawf A. A. Kahtan, G. Sharath, K. R. Vasuki장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제3호
이 간행물의 다른 논문 (12건)
Fibonacci functional sequence generating functionsA. G. Shannonpp. 285-292Some new inequalities for the -gamma and related functionsMOHAMED EL BACHRAOUI, Jozsef Sandorpp. 293-310On the results of nonlocal Hilfer fractional semilinear differential inclusionsR. Subashini, C. Ravichandranpp. 311-330Wiener's lemma for Banach algebras of infinite matrices of GBS class한혁, 신창언pp. 339-348An iterative method for common solution to various problemsIBRAHIM KARAHAN, SAFEER HUSAIN KHANpp. 349-364
