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Transactions of the American Mathematical Society

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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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    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. The Bateman Manuscript Project, Higher transcendental functions, Vol. 1, New York, McGraw-Hill Book Co., 1953. C. Fox, A generalization of the Fourier Bessel integral transform, Proc. London Math. Soc. Ser. 2 vol. 29 (1929) pp. 401-452. 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.
  • Roop Narain, A Fourier kernel, Math. Z. 70 (1958/59), 297–299. MR 104988, DOI
  • E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford, University Press, 1937.
  • 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

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Article copyright: © Copyright 1961 American Mathematical Society