论文信息 - An analytic method for convergence acceleration of certain hypergeometric series

An analytic method for convergence acceleration of certain hypergeometric series

A method is presented for convergence acceleration of the generalized hypergeometric series 3 F 2 with the argument ± 1, using analytic properties of their terms. Iterated transformation of the series is performed analytically, which results in obtaining new fast converging expansions for some special functions and mathematical constants

Stefan Paszkowski | Stanisław Lewanowicz | S. Lewanowicz | S. Paszkowski

[1] W. N. Bailey. Contiguous Hypergeometric Functions of the Type 3F2(1) , 1954 .

[2] Claude Brezinski,et al. Extrapolation methods - theory and practice , 1993, Studies in computational mathematics.

[3] D. F. Hays,et al. Table of Integrals, Series, and Products , 1966 .

[4] C. W. Clenshaw,et al. The special functions and their approximations , 1972 .

[5] M. Abramowitz,et al. Mathematical functions and their approximations , 1975 .

[6] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[7] Y. Luke,et al. Integrals of Jacobi functions , 1982 .

[8] Y. Luke. Rational approximations for the logarithmic derivative of the gamma function , 1971 .

[9] Avram Sidi,et al. Analysis of convergence of the $T$-transformation for power series , 1980 .

[10] K. Knopp. Theory and Application of Infinite Series , 1990 .

[11] A. Erdélyi,et al. Higher Transcendental Functions , 1954 .

[12] Avram Sidi,et al. Convergence properties of some nonlinear sequence transformations , 1979 .

[13] Ernst Joachim Weniger,et al. Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series , 1989 .

[14] C. Brezinski,et al. Extrapolation methods , 1992 .

[15] Jet Wimp,et al. Computation with recurrence relations , 1986 .