论文信息 - Asymptotic and generating relations for the q-Jacobi and 4φ3 polynomials - 字舞流文

Asymptotic and generating relations for the q-Jacobi and 4φ3 polynomials

Abstract Generating functions, explicit representations, and uniform asymptotic formulas are derived for the little q -Jacobi polynomials, the big q -Jacobi polynomials, and the 4 φ 3 polynomials.

Mourad E. H. Ismail | James A. Wilson | M. Ismail

[1] James A. Wilson. Some Hypergeometric Orthogonal Polynomials , 1980 .

[2] W. N. Bailey,et al. Generalized hypergeometric series , 1935 .

[3] W. Rheinboldt,et al. Generalized hypergeometric functions , 1968 .

[4] F. Olver. Asymptotics and Special Functions , 1974 .

[5] George E. Andrews,et al. On the $q$-analog of Kummer’s theorem and applications , 1973 .

[6] Reproducing kernels for $q$-Jacobi polynomials , 1977 .

[7] Mourad E. H. Ismail,et al. ORTHOGONAL POLYNOMIALS ASSOCIATED WITH THE ROGERS-RAMANUJAN CONTINUED FRACTION , 1983 .

[8] Dennis Stanton,et al. A short proof of a generating function for Jacobi polynomials , 1980 .

[9] Mourad E. H. Ismail,et al. The zeros of basic Bessel functions, the functions Jv + ax(x), and associated orthogonal polynomials☆ , 1982 .

[10] Richard Askey,et al. A Set of Orthogonal Polynomials That Generalize the Racah Coefficients or 6 - j Symbols. , 1979 .

[11] D. B. Sears. On the Transformation Theory of Basic Hypergeometric Functions , 1950 .

[12] G. A. Watson. A treatise on the theory of Bessel functions , 1944 .

[13] T. Chihara,et al. Convolutions of Orthonormal Polynomials , 1976 .

[14] T. A. Bromwich. An Introduction To The Theory Of Infinite Series , 1908 .