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 and J. Wimp,*Jacobi polynomial expansions of a generalized hypergeometric function over a semi-infinite ray*, Math. Comp.**17**(1963), 395–404. MR**0157014**, https://doi.org/10.1090/S0025-5718-1963-0157014-4**[3]**R. K. Saxena,*Some formulae for the 𝐺-function*, Proc. Cambridge Philos. Soc.**59**(1963), 347–350. MR**0148952****[4]**Reference 1, p. 208, formula (5).**[5]**C. S. Meijer,*On the 𝐺-function. I*, Nederl. Akad. Wetensch., Proc.**49**(1946), 227–237 = Indagationes Math. 8, 124–134 (1946). MR**0017452****[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*, SIAM J. Numer. Anal.**3**(1966), 390–409. MR**0203312**, https://doi.org/10.1137/0703034**[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]**G. Németh,*Chebyshev expansions for Fresnel integrals*, Numer. Math.**7**(1965), 310–312. MR**0185805**, https://doi.org/10.1007/BF01436524**[12]**Rudolph E. Langer,*Turning points in linear asymptotic theory*, Bol. Soc. Mat. Mexicana (2)**5**(1960), 1–12. MR**0120429****[13]**H. L. Turrittin,*The formal theory of systems of irregular homogeneous linear difference and differential equations*, Bol. Soc. Mat. Mexicana (2)**5**(1960), 255–264. MR**0136888**

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

Article copyright:
© Copyright 1967
American Mathematical Society