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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The $ G$ and $ H$ functions as symmetrical Fourier kernels


Author: Charles Fox
Journal: Trans. Amer. Math. Soc. 98 (1961), 395-429
MSC: Primary 33.21
MathSciNet review: 0131578
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  • [1] E. W. Barnes, The asymptotic expansion of integral functions defined by generalized hypergeometric series, Proc. London Math. Soc. Ser. 2 vol. 5 (1907) pp. 59-117.
  • [2] The Bateman Manuscript Project, Higher transcendental functions, Vol. 1, New York, McGraw-Hill Book Co., 1953.
  • [3] C. Fox, A generalization of the Fourier Bessel integral transform, Proc. London Math. Soc. Ser. 2 vol. 29 (1929) pp. 401-452.
  • [4] C. S. Meijer, On the G-function, Proc. Nederl. Akad. Wetensch. vol. 49 (1946) pp. 227-237, 344-356, 457-469, 632-641, 765-772, 936-943, 1062-1072, 1165-1175.
  • [5] Roop Narain, A Fourier kernel, Math. Z. 70 (1958/1959), 297–299. MR 0104988 (21 #3735)
  • [6] E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford, University Press, 1937.
  • [7] E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469 (97k:01072)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1961-0131578-3
PII: S 0002-9947(1961)0131578-3
Article copyright: © Copyright 1961 American Mathematical Society