Rational approximations to generalized hypergeometric functions

Author:
Jerry L. Fields

Journal:
Math. Comp. **19** (1965), 606-624

MSC:
Primary 33.20

DOI:
https://doi.org/10.1090/S0025-5718-1965-0194620-7

MathSciNet review:
0194620

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References | Similar Articles | Additional Information

**[1]**R. Bellman, "On approximate expressions for the exponential integral and the error function,"*J. Math and Phys.*, v. 30, 1952, pp. 226-231. MR**13**, 690. MR**0046131 (13:690f)****[2]**Y. L. Luke, "On economic representations of transcendental functions,"*J. Math. and Phys.*, v. 38, 1960, pp. 279-294. MR**22**#3829. MR**0112984 (22:3829)****[3]**C. Lanczos, "Trigonometric interpolation of empirical and analytical functions,"*J. Math. and Phys.*, v. 17, 1938, pp. 123-199.**[4]**C. Lanczos,*Tables of Chebyshev Polynomials**and*, National Bureau of Standards, AMS9, December, 1952.**[5]**C. Lanczos,*Applied Analysis*, Prentice-Hall, Englewood Cliffs, N. J., 1956, MR**18**, 823. MR**0084175 (18:823c)****[6]**G. N. Watson,*A Treatise on the Theory of Bessel Functions*, 2nd ed., Cambridge Univ. Press, New York and Macmillan, New York, pp. 210-212, MR**6**, 64. MR**1349110 (96i:33010)****[7]**A. Erdélyi, et al.,*Higher Transcendental Functions*, Vol. I, McGraw-Hill, New York, 1953. MR**15**, 419.**[8]**E. W. Barnes, "The asymptotic expansion of integral functions defined by generalized hypergeometric series,"*Proc. London Math. Soc.*(2), v. 5, 1907, pp. 59-116.**[9]**Y. L. Luke,*Integrals of Bessel Functions*, McGraw-Hill, New York, 1962, pp. 14-17. MR**25**#5198. MR**0141801 (25:5198)****[10]**J. L. Fields & Y. L. Luke, "Asymptotic expansions of a class of hypergeometric polynomials with respect to the order,"*J. Math. Anal. Appl.*, v. 6, 1963, pp. 394-403. MR**26**#6446. MR**0148950 (26:6446)****[11]**G. Szegö,*Orthogonal Polynomials*, Amer. Math. Soc. Colloq. Publ. Vol. 23, Amer. Math. Soc., Providence, R. I., 1939; rev. ed., 1959. MR**1**, 14; MR**21**#5029. MR**0106295 (21:5029)****[12]**J. L. Fields & Y. L. Luke, "Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. II,"*J. Math. Anal. Appl.*, v. 7, 1963, pp. 440-451. MR**28**#256. MR**0157015 (28:256)****[13]**C. S. Meijer, "On the -function. I, II,"*Nederl. Akad. Wetensch. Proc.*, v. 49, 1946, p. 234 and pp. 344-346 =*Indag. Math.*, v. 8, 1946, p. 133 and pp. 213-225. MR**8**, 156. MR**0017452 (8:156a)**

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DOI:
https://doi.org/10.1090/S0025-5718-1965-0194620-7

Article copyright:
© Copyright 1965
American Mathematical Society