The asymptotic representation of a class of -functions for large parameter

Author:
Jet Wimp

Journal:
Math. Comp. **21** (1967), 639-646

MSC:
Primary 33.21

DOI:
https://doi.org/10.1090/S0025-5718-1967-0223617-5

MathSciNet review:
0223617

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References | Similar Articles | Additional Information

**[1]**A. Erdélyi, et al.,*Higher Transcendental Functions*, Vol. 1, McGraw-Hill, New York, 1953, Chapter 5. MR**15**, 419.**[2]**Y. L. Luke & Jet Wimp, "Jacobi polynomial expansions of a generalized hypergeometric function over a semi-infinite ray,"*Math. Comp.*, v. 17, 1963, pp. 395-404. MR**28**#255. MR**0157014 (28:255)****[3]**R. K. Saxena, "Some formulae for the*G*-function,"*Proc. Cambridge Philos. Soc.*, v. 59, 1963, pp. 347-350. MR**26**#6448. MR**0148952 (26:6448)****[4]**Reference 1, p. 208, formula (5).**[5]**C. S. Meijer, "On the*G*-function. I,"*Nederl. Akad. Welensch.*, v. 49, 1946, p. 234, formulae (22)-(24). MR**8**, 156. MR**0017452 (8:156a)****[6]**Géza Németh, "Polynomial approximations to the function ," Reports of the Central Institute for Physics, Budapest, 1965.**[7]**G. F. Miller, "On the convergence of the Chebyshev series for functions possessing a singularity in the range of representation,"*J. Soc. Indust. Appl. Math. Ser. Numer. Anal.*, v. 3, 1966, pp. 390-409. MR**0203312 (34:3165)****[8]**George Birkhoff & W. J. Trjitzinsky, "The analytic theory of singular difference equations,"*Acta Math.*, v. 60, 1932, pp. 1-89.**[9]**Reference 1, p. 218.**[10]**Géza Németh, (a) "Chebyshev expansions of Bessel functions. and ";(b)"Chebyshev expansions of integral sine and integral cosine functions," same reports as Reference 6.**[11]**Géza Németh, "Chebyshev expansions for Fresnel integrals,"*Numer. Math.*, v. 7, 1965, pp. 310-312. MR**32**#3265. MR**0185805 (32:3265)****[12]**R. E. Langer, "Turning points in linear asymptotic theory,"*Bol. Soc. Mat. Mexicana*(2), v. 5, 1960, pp. 1-12. MR**22**#11183. MR**0120429 (22:11183)****[13]**H. L. Turrittin, "The formal theory of systems of irregular homogeneous linear difference and differential equations,"*Bol. Soc. Mat. Mexicana*, (2), v. 5, 1960, pp. 255-264. MR**25**#349. MR**0136888 (25:349)**

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DOI:
https://doi.org/10.1090/S0025-5718-1967-0223617-5

Article copyright:
© Copyright 1967
American Mathematical Society