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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.
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참고문헌 (24)
참고문헌 신청
A. K. Ibrahim / / Contiguous relations for 2F1 hypergeometric series
C. F. Gauss / 1876 / Disquisitiones generales circa seriem infinitam / Comm. soc. reg. sci. Gott. rec. II : 123 ~ 162
D. Gupta / 1996 / Contiguous relations, basic hypergeometric functions and orthogonal polynomials III. Associated contiguous dual q?Hann polynomials / J. Comput. Appl. Math.
D. Gupta / 1998 / Contiguous relations, continued fractions and orthogonality / Trans. Amer. Math. Soc. 350 (2) : 679 ~ 808
E. D. Rainville / 1945 / 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 : 714 ~ 7
C. F. Gauss / 1876 / Disquisitiones generales circa seriem infinitam / Comm. soc. reg. sci. Gott. rec. II : 123 ~ 162
D. Gupta / 1996 / Contiguous relations, basic hypergeometric functions and orthogonal polynomials III. Associated contiguous dual q?Hann polynomials / J. Comput. Appl. Math.
D. Gupta / 1998 / Contiguous relations, continued fractions and orthogonality / Trans. Amer. Math. Soc. 350 (2) : 679 ~ 808
E. D. Rainville / 1945 / 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 : 714 ~ 7
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