On the computations of contiguous relations for _{2}F_{1} hypergeometric series
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous relations range from the evaluation of hypergeometric series to the derivation of summation and transformation formulas for such series. In this paper, a general formula joining three Gauss functions of the form$_{2}F_{1}[a_{1},a_{2};a_{3};z] with arbitrary integer shifts is presented. Our analysis depends on using shifted operators attached to the three parameters a_{1},a_{2} and a_{3}. We also, discussed the existence condition of our formula.
Abstract
Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous relations range from the evaluation of hypergeometric series to the derivation of summation and transformation formulas for such series. In this paper, a general formula joining three Gauss functions of the form$_{2}F_{1}[a_{1},a_{2};a_{3};z] with arbitrary integer shifts is presented. Our analysis depends on using shifted operators attached to the three parameters a_{1},a_{2} and a_{3}. We also, discussed the existence condition of our formula.
참고문헌 (24)
- M. Abramowitz, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing" (1972), Dover
- P. Agarwal, "Contiguous relations for bilateral basic hypergeometric series", Int. J. Math. Sci., 3, pp.375~388 (2004)
- G. E. Andrews, "Special Functions" (1999), Cambridge University Press
- G. Gasper, "Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications" (1990), Cambridge University Press
- C. F. Gauss, "Disquisitiones generales circa seriem infinitam", Comm. soc. reg. sci. Gött. rec., II, pp.123~162 (1876)
- D. Gupta, "Contiguous relations, basic hypergeometric functions and orthogonal polynomials III. Associated contiguous dual q−Hann polynomials", J. Comput. Appl. Math., 68(1), pp.115~149 (1996)
- D. Gupta, "Contiguous relations, continued fractions and orthogonality", Trans. Amer. Math. Soc., 350(2), pp.679~808 (1998)
- A. K. Ibrahim, "Contiguous relations for 2F1 hypergeometric series", ~, Submitted for Publications
- M. Ismail, "Contiguous relations, basic hypergeometric functions and orthogonal polynomials", J. Math. Anal. Appl., 141(2), pp.349~372 (1989)
- J. L. Lavoie, "Generalizations of Watson’s theorem on the sum of 3F2", Indian J. Math., 32, pp.23~32 (1992)
- J. L. Lavoie, "Generalizations of Whipple’s theorem on the sum of a 3F2", J. Comput. Appl. Math., 72, pp.293~300 (1996)
- J. L. Lavoie, "Generalizations of Dixon’s theorem on the sum a 3F2", Math. Comp., 63, pp.367~376 (1994)
- W. Miller, Jr., "Lie theory and generalizations of hypergeometric functions", SIAM J. Appl. Math., 25(1), pp.226~235 (1973)
- "Inderdiscip. Inform. Sci.", 1996, 63~74
- Contiguous Relations and Creative Telescopy, "P. Paule", RISC, ~, pp.Technical report (2001)
- E. D. Rainville, "The contiguous function relations for pFq with applications to Bateman’s Ju,vn and Rice’s Hn(ζ, p, v)", Bull. Amer. Math. Soc. Ser., 251, pp.714~723 (1945)
- E. D. Rainville, "Special Functions" (1960), The Macmillan Company
- M. A. Rakha, "On the contiguous relations of hypergeometric series", J. of Comput. Appl. Math., 192, pp.396~410 (2006)
- M. A. Rakha, "Contiguous relations and their computations for 2F1 hypergeometric series", Comput. Math. Appl., (56), pp.1918~1926 (2008)
- K. C. Richards, "Shap power mean bounds for Gaussian hypergeometric functions", J. Math. Anal. Appl., 38, pp.303~313 (2005)
- R. Vidúnas, "A generalization of Kummer’s identity", Rocky Mountain J. Math., 32(2), pp.919~935 (2002)
- R. Vidúnas, "Contiguous relations of hypergeometric series", J. Math. Anal. Appl., 135, pp.507~519 (2003)
- R. Vid´unas, "Contiguous relations of hypergeometric series", J. Math. Anal. Appl, 135, pp.507~519 (2003)