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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**[1]**Richard Bellman,*On approximate expressions for the exponential integral and the error function*, J. Math. Physics**30**(1952), 226–231. MR**0046131****[2]**Yudell L. Luke,*On economic representations of transcendental functions*, J. Math. and Phys.**38**(1959/60), 279–294. MR**112984****[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]**Cornelius Lanczos,*Applied analysis*, Prentice Hall, Inc., Englewood Cliffs, N. J., 1956. MR**0084175****[6]**G. N. Watson,*A treatise on the theory of Bessel functions*, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR**1349110****[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]**Yudell L. Luke,*Integrals of Bessel functions*, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1962. MR**0141801****[10]**Jerry L. Fields and Yudell L. Luke,*Asymptotic expansions of a class of hypergeometric polynomials with respect to the order*, J. Math. Anal. Appl.**6**(1963), 394–403. MR**148950**, https://doi.org/10.1016/0022-247X(63)90020-9**[11]**Gabor Szegö,*Orthogonal polynomials*, American Mathematical Society Colloquium Publications, Vol. 23. Revised ed, American Mathematical Society, Providence, R.I., 1959. MR**0106295****[12]**Jerry L. Fields and Yudell L. Luke,*Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. II*, J. Math. Anal. Appl.**7**(1963), 440–451. MR**157015**, https://doi.org/10.1016/0022-247X(63)90066-0**[13]**C. S. Meijer,*On the 𝐺-function. I*, Nederl. Akad. Wetensch., Proc.**49**(1946), 227–237 = Indagationes Math. 8, 124–134 (1946). MR**17452**

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

Article copyright:
© Copyright 1965
American Mathematical Society